Short answer
Jesus, the son of Mary, himself. The Prophet (ﷺ) swore that the son of Mary will soon come down among the Muslims as a just ruler. The Qur'an says that the People of the Book will believe in him before his death (4:159). It also speaks of him as a sign of the Hour (43:61), as the early commentators read it. Ibn Abbas, a Companion, read 43:61 this way. In one of two reports from him, he read 4:159 this way too. The hadith names him and says what he will do. It does not speak of another man in his likeness. He returns as a follower of Muhammad (ﷺ), with no new law. He keeps the prophethood he was given before Muhammad (ﷺ). No one is made a prophet after Muhammad (ﷺ), so the finality of prophethood stands. Ahmadi readers see the promise fulfilled in Mirza Ghulam Ahmad. This page shows what the texts say.
Full explanation
The Qur'an: the same Jesus, raised and returning
The Qur'an says Allah (﷾) raised Jesus up to Himself. It says that every one of the People of the Book will believe in him before his death. It also speaks of him as a sign of the Hour. Al-Tabari records how the early scholars read these verses. On 43:61, Ibn Abbas said the sign of the Hour is the coming down of Jesus. On 4:159 he is reported both ways. In one report, "before his death" means before the death of Jesus. In another, it means before the death of each person of the Book. Al-Tabari judges that before the death of Jesus is the sounder reading. Al-Hasan al-Basri said: by Allah (﷾), he is alive now with Allah (﷾), and when he comes down they will all believe in him. Ibn Kathir calls this reading the truth.
“Nay, Allah raised him up unto Himself; and Allah is Exalted in Power, Wise;-”
“And there is none of the People of the Book but must believe in him before his death; and on the Day of Judgment he will be a witness against them;-”
“And (Jesus) shall be a Sign (for the coming of) the Hour (of Judgment): therefore have no doubt about the (Hour), but follow ye Me: this is a Straight Way.”
Al-Tabari records the view that "before his death" means before the death of Jesus: when he comes down to kill the False Messiah, all the creeds will become one. He gives it from Ibn Abbas through Sa'id ibn Jubayr ("before the death of Jesus son of Mary"), and from Abu Malik, Qatada and al-Hasan. Al-Hasan says: by Allah, he is alive now with Allah, and when he comes down they will all believe in him. He also records a second view, that it means before the death of each person of the Book, and gives this too from Ibn Abbas, through Ikrima. His own judgement is that the sounder reading is before the death of Jesus.
Al-Tabari records the view that the "it" in "a Sign of the Hour" is Jesus: his appearing is a sign that the Hour is near. He reports it from Ibn Abbas ("the coming down of Jesus son of Mary", and that Ibn Abbas read 'alam, a sign), and from Abu Malik, al-Hasan, Mujahid, Qatada, al-Suddi and al-Dahhak.
Ibn Kathir gives the reports that "before his death" means before the death of Jesus, from Ibn Abbas, Abu Malik, al-Hasan al-Basri, Qatada and Ibn Zayd. They say it happens when Jesus comes down before the Day of Judgment. He calls this view "the truth" and says he will prove it with decisive evidence.
The Prophet (ﷺ) names him
The Prophet (ﷺ) swore by Allah (﷾) that the son of Mary will soon come down among you as a just ruler. Abu Hurayra, a Companion, then recited 4:159. Another report says: how will you be when the son of Mary comes down among you and your imam is from among you? Muslim's long report of the False Messiah says that Allah (﷾) will send Jesus, son of Mary, who will come down and overcome him. He gave details. Jesus comes down by the white minaret east of Damascus, in two lightly dyed garments, with his hands on the wings of two angels. He catches the False Messiah at the gate of Ludd and kills him. Ibn Kathir says these reports are mutawatir: passed on by so many that they cannot be mistaken. Each names the son of Mary. None says: a man like the son of Mary.
Abu Huraira reports that the Prophet (ﷺ) swore that the son of Mary will soon descend among the Muslims as a just ruler. He will break the cross, kill the swine and end the jizya, and wealth will be so plentiful that no one will accept it. Abu Huraira then recited Qur'an 4:159: none of the People of the Book but will believe in him before his death.
Abu Hurayra reports that the Prophet (ﷺ) asked his companions how they would be when the son of Mary descends among them while their own imam is among them.
Al-Nawwas ibn Sam'an reports the Prophet's (ﷺ) long description of the False Messiah (al-Dajjal). Allah will then send Jesus son of Mary, who will descend at the white minaret east of Damascus, pursue the False Messiah, catch him at the gate of Ludd and kill him. The hadith calls Jesus a prophet of Allah who, with his companions, prays to Allah for help.
Ibn Kathir says the sound view is that the "it" in "a Sign of the Hour" refers to Jesus, and the meaning is his coming down before the Day of Judgment. He reports it from Mujahid, Abu Hurayra, Ibn Abbas and others. He adds that the hadiths from the Prophet (ﷺ) that Jesus will come down before the Day of Judgment as a just ruler are mutawatir.
What kind of man he is
The same reports show what kind of man he is. The Prophet (ﷺ) said there was no prophet between himself and Jesus. Jesus is the prophet nearest to him. In Muslim, when the Muslims' leader invites Jesus to lead the prayer, he declines, because Allah (﷾) has honoured this community with leaders from among itself. A narrator explains that he will lead them by the Book of their Lord and the Sunnah of their Prophet. So he comes as a follower of Muhammad (ﷺ), and he brings no new law. He does not lose his prophethood, which Allah (﷾) gave him before Muhammad (ﷺ). No one is made a prophet after Muhammad (ﷺ), and Jesus follows his law. The Seal of the Prophets is untouched.
Abu Hurayra reports that the Prophet (ﷺ) said he was the nearest of all people to the son of Mary. The prophets are brothers with one father, he said, and there was no prophet between him and Jesus.
Jabir reports that the Prophet (ﷺ) said Jesus son of Mary will descend, and the Muslims' leader will invite him to lead the prayer. Jesus will decline and say that the Muslims' leaders are from among themselves, an honour from Allah to this community.
In 155a Abu Huraira reports that the Prophet (ﷺ) swore the son of Mary will soon descend as a just judge, break the cross, kill the swine and end the jizya. In 155f the Prophet asks how it will be when the son of Mary descends and leads the Muslims as one of them; the narrator Ibn Abi Dhi'b explains that he will lead them by the Book of their Lord and the Sunnah of their Prophet.
“Muhammad is not the father of any of your men, but (he is) the Messenger of Allah, and the Seal of the Prophets: and Allah has full knowledge of all things.”
The Ahmadi reading: a Messiah in the likeness of Jesus
Mirza Ghulam Ahmad of Qadian taught that Jesus died and will not return. In his view the promised Messiah is a man like Jesus, born in the community. He wrote that in his early book, Barahin-e-Ahmadiyya, he had said that Jesus, son of Mary, would descend from heaven. A body of Muslims held that belief, he writes, and he held it too. Later, he writes, revelations led him to say that he himself was the Messiah who was to come. He argued from Elijah: the Jews expected Elijah himself to return before the Messiah, but he did not come in person. The community's WhyAhmadi site reads the hadith of the imam "from among you" as pointing to the same man. Another community page holds that the Messiah and the Mahdi are one man.
Mirza Ghulam Ahmad writes that in Barahin-e-Ahmadiyya he wrote that Jesus, son of Mary, would descend from heaven, because a body of Muslims held that belief and he held it too. Later, he writes, revelations led him to say that he himself was the Messiah who was to come. On p. 184 he writes that the title Prophet was bestowed on him with the proviso that he is a prophet in one aspect and an ummati (follower of the Prophet (ﷺ)) in another.
Mirza Ghulam Ahmad writes that the Jews said Jesus would appear only after Elijah had returned to earth, and asks whether Elijah came. He uses this to argue that promised signs need not be fulfilled in the literal way people expect, and warns Muslims against the Jews' error of insisting on their own reading.
The community's page answers those who say no prophet is needed because the Qur'an and the Sunnah are preserved. It says Allah and the Prophet (ﷺ) do not agree, since the Prophet told us Jesus will come. It argues that Muslims still need guidance, and that the only way to bring them back to the right path is for Allah to send another prophet in Islam. It reads the hadith that Jesus will descend among Muslims with an imam from among them as a metaphor for the coming of Mirza Ghulam Ahmad.
The community's page holds that the Messiah and the Mahdi are one person, not two. It cites a report in Ibn Majah, "the Mahdi is no other than the Messiah", and argues that the two are the same man who first appears as a reformer and then declares himself the Promised Messiah.
Elijah and John: the New Testament says it is a likeness
Take the Elijah example on its own terms. Matthew reports Jesus saying of John the Baptist, "if ye will receive it, this is Elias". But Luke and John make clear it is a likeness. The angel says John will go before the Lord "in the spirit and power of Elias". And when John is asked, "Art thou Elias?", he answers, "I am not". The reports about Jesus carry no such mark. They say that the son of Mary himself will come down. The Qur'an says the People of the Book will believe in him before his own death. Nothing says: in the spirit of Jesus.
“Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the Lord:”
“And if ye will receive it, this is Elias, which was for to come.”
“Then the disciples understood that he spake unto them of John the Baptist.”
“And he shall go before him in the spirit and power of Elias, to turn the hearts of the fathers to the children, and the disobedient to the wisdom of the just; to make ready a people prepared for the Lord.”
“And they asked him, What then? Art thou Elias? And he saith, I am not. Art thou that prophet? And he answered, No.”
Is the Messiah also the Mahdi?
The Mahdi ("the rightly guided one") is a leader the Prophet (ﷺ) foretold for the last days. The Ahmadi page holds that the Messiah and the Mahdi are one man. It cites a report in Ibn Majah that there is no Mahdi but Jesus. That report is graded very weak. Sound reports in Abu Dawud describe the Mahdi as a man of the Prophet's (ﷺ) family. He is from the descendants of Fatima, and he will fill the earth with justice. The Messiah is the son of Mary, who was sent before. They are two different men.
The community's page holds that the Messiah and the Mahdi are one person, not two. It cites a report in Ibn Majah, "the Mahdi is no other than the Messiah", and argues that the two are the same man who first appears as a reformer and then declares himself the Promised Messiah.
Anas ibn Malik is reported to have said that the Prophet (ﷺ) said the Hour would come upon the worst of people, and that the only Mahdi is Jesus son of Mary. Al-Albani grades the report very weak.
Ali ibn Abi Talib reports that the Prophet (ﷺ) said: if only one day of this world remained, Allah would raise up a man from my family who would fill the earth with justice as it has been filled with oppression.
Umm Salama reports that the Prophet (ﷺ) said: the Mahdi will be of my family, of the descendants of Fatima.
The belief of the first Muslims
The belief rests on the Qur'an and the Prophet's (ﷺ) words, which have not changed. It is the belief of Companions who reported the hadith, such as Abu Hurayra and Ibn Abbas. It is also the belief of the commentators who followed them, from al-Hasan al-Basri to Ibn Kathir. Mirza Ghulam Ahmad himself wrote that the Muslims of his day held it.
Mirza Ghulam Ahmad writes that in Barahin-e-Ahmadiyya he wrote that Jesus, son of Mary, would descend from heaven, because a body of Muslims held that belief and he held it too. Later, he writes, revelations led him to say that he himself was the Messiah who was to come. On p. 184 he writes that the title Prophet was bestowed on him with the proviso that he is a prophet in one aspect and an ummati (follower of the Prophet (ﷺ)) in another.
Al-Tabari records the view that the "it" in "a Sign of the Hour" is Jesus: his appearing is a sign that the Hour is near. He reports it from Ibn Abbas ("the coming down of Jesus son of Mary", and that Ibn Abbas read 'alam, a sign), and from Abu Malik, al-Hasan, Mujahid, Qatada, al-Suddi and al-Dahhak.
Ibn Kathir says the sound view is that the "it" in "a Sign of the Hour" refers to Jesus, and the meaning is his coming down before the Day of Judgment. He reports it from Mujahid, Abu Hurayra, Ibn Abbas and others. He adds that the hadiths from the Prophet (ﷺ) that Jesus will come down before the Day of Judgment as a just ruler are mutawatir.
Where this leaves the reader
The texts speak of the son of Mary himself. A reader who loves Jesus as a prophet of Allah (﷾) can hold two truths. Jesus lives with Allah (﷾). He will come back as a servant of Allah (﷾) and a follower of Muhammad (ﷺ). Muslims hold that believing Muhammad (ﷺ) to be the last prophet is part of what the testimony of faith affirms. So accepting a prophet after him contradicts it. We say this plainly, and with warmth for every reader who loves both Jesus and Muhammad (ﷺ). The door of the Muslim community is open to all who hold to the testimony.
“Nay, Allah raised him up unto Himself; and Allah is Exalted in Power, Wise;-”
Abu Huraira reports that the Prophet (ﷺ) swore that the son of Mary will soon descend among the Muslims as a just ruler. He will break the cross, kill the swine and end the jizya, and wealth will be so plentiful that no one will accept it. Abu Huraira then recited Qur'an 4:159: none of the People of the Book but will believe in him before his death.
“Muhammad is not the father of any of your men, but (he is) the Messenger of Allah, and the Seal of the Prophets: and Allah has full knowledge of all things.”
Perspectives
The Ahmadi view
Ahmadis hold that Jesus died and will not return. They teach that the promised Messiah is a man in the likeness of Jesus, born in the community. They hold that Mirza Ghulam Ahmad of Qadian is that Messiah.
The promised Messiah is a man in the likeness of Jesus, born in the community. He is not Jesus himself.
Rebuttal
The Prophet (ﷺ) swore that the son of Mary himself will come down, and Abu Hurayra recited 4:159 about him. Ibn Abbas read 43:61 as the coming down of Jesus, son of Mary. The hadith names the son of Mary, never a man like him. The details he gave leave no room for a figure: a minaret, two garments, the wings of two angels, the gate of Ludd.
As Elijah's return was fulfilled in John the Baptist, so Jesus' return is fulfilled in a man like him.
Rebuttal
Luke and John make clear that John is Elijah only "in the spirit and power of Elias", and John himself said "I am not". The hadith has no such mark. It names the son of Mary, and Abu Hurayra recited 4:159 about him.
The hadith says the Messiah will be "your imam from among you", so he is born among the Muslims.
Rebuttal
In Bukhari's wording the son of Mary comes down while the Muslims' own imam is among them. Muslim records that this imam invites Jesus to lead, and he declines. In another of Muslim's wordings Jesus leads them "from among you". The early narrator Ibn Abi Dhi'b explains it: he leads by the Book of your Lord and the Sunnah of your Prophet. Either way, the one who comes down is named the son of Mary. "From among you" means following this community's law, not being born in it.
Jesus died, so he cannot return.
Rebuttal
Muslims agree he will die, after his return: he will stay forty years, then die, and the Muslims will pray over him. The only question is when. The page on Kashmir answers this in full. In short, tawaffa means to take in full, and the Qur'an uses it for sleep. Verse 4:158 says Allah (﷾) raised him. Ibn Abbas read 43:61 as his return, and in one report 4:159 too.
A hadith says there is no Mahdi but Jesus, so the Mahdi and the Messiah are one man.
Rebuttal
That report in Ibn Majah is graded very weak. Sound reports in Abu Dawud describe the Mahdi as a man of the Prophet's (ﷺ) family, from the descendants of Fatima. He fills the earth with justice. That makes two different men: the Mahdi, and the son of Mary who comes down.
The Islamic perspective
The Messiah who will return is Jesus, son of Mary, himself. The Qur'an and the Prophet's (ﷺ) words name him, and the first commentators read them so. He comes as a follower of Muhammad (ﷺ) with no new law.
The Qur'an says Allah (﷾) raised Jesus up to Himself. It says the People of the Book will believe in him before his death.
The Qur'an calls Jesus a sign of the Hour, and Ibn Abbas read this as his coming down.
The Prophet (ﷺ) swore that the son of Mary will soon come down among the Muslims as a just ruler.
The reports name the son of Mary, who comes down and follows the Muslims' Book and Sunnah.
Jesus is the prophet nearest to Muhammad (ﷺ), and he returns to lead by the Book and the Sunnah.