The internal evidence of the authorship is found in four passages in the Book of Revelation. It is in these four passages that the author refers to himself as "John".
Rev 1:1 This is the revelation of Jesus Christ, which God gave him to show his servants the things that must happen soon. He made it known by sending his angel to his servant John,
Rev 1:4 From John to the seven churches in Asia.......
Rev 1:9"I, John, both your brother and companion in tribulation, and in the kingdom and patience of Jesus Christ, was on the island that is called Patmos for the word of God and for the testimony of Jesus Christ."
Rev 22:8 "Now I, John, saw and heard these things. And when I heard and saw, I fell down to worship before the feet of the angel who showed me these things."
Also the very title of the Book includes in it the name John. This title "occurs in several MSS, including the Codex Sinaiticus".
Additionally, the fingerprints of John the apostle are all over the apocalypse. For example, Jesus Christ as the Lamb is referred in both these books. Also, John, and John alone, identifies Jesus as the Word, or Logos (John 1:1, 14; Revelation 19:13). Likewise, John alone identifies Jesus as the true witness (John 5:31–47; 8:14–18; Revelation 2:13; 3:14), and it is John who most exploits the Mosaic requirement of two witnesses (John 8:12–30; Revelation 11:1–12).
With mention of this single name as John, with no attempt to clarify any further on it, obviously indicates that he was well-known to his first readers, to whom no further identification was necessary. This conclusion is supported by most ancient historians.
Revelation has long been attributed to the author of John's Gospel, in spite of the differences in style of writing. The reason for this difference in style could possibly be that, the book of revelation was revealed to John the apostle at his old age and was possibly penned with the help of someone who was not good in Greek language. Since Domitian died in A.D. 96, the date attributed to the book of Revelation coincides with this date by which time John would have been quite old (Date of death of John is taken as 100AD at the age of 94). The evidence against John the Apostle being the author is minimal, and largely based on grammatical and writing style differences with the John’s Gospel.
Homer Hailey states concerning this matter:
"Although a few relatively early writers raised the question of authorship, the Apostle John's composition of Revelation was never seriously questioned until modern nineteenth-century liberal criticism."
Early church fathers were unanimous that it was John the apostle. As one examines this segment of history, one needs to be reminded that the further away from the first century one gets the lesser reliable evidence to know about the correctness of any claim on this issue.
Justin Martyr (A.D. 110-165) in his Dialogue with Trypho the Jew (LXXXI) says. "There was a certain man with us, whose name was John, one of the apostles of Christ, who prophesied by revelation," and then refers to the thousand years, the resurrection and the Judgment of Revelation 20. Again Justin Martyr (100-165 A.D.) quotes John the Apostle that Jesus Christ would dwell in Jerusalem one thousand years.
Irenaeus (120-200 A.D.) quoted in every chapter of Revelation. Irenaeus who had heard Polycarp, a disciple of John the apostle, wrote in his Against Heresies (IV. xx. 11), "John, also the Lord's Disciple ..... says in the Apocalypse," and then quotes profusely from that Book. (11) Having thus identified him as the "Lord's Disciple". Irenaeus says later: "In a still clearer light has John, in the Apocalypse, revealed certain things," which the writer proceeds to discuss (V.xxi 1).
Tertullian (155-220 A.D.), sometimes called "the Father of Latin Christianity," a voluminous writer, also quotes from almost every chapter of Revelation and attributes John the Apostle as author. He wrote five books Against Marcion Hippolytus (170-235 A.D.) also attributed Revelation to John, he quotes Revelation chapter 17 and 18 a great deal. In book III. xxv, Tertullian writes of the Jerusalem let down from heaven. He quotes Paul, who called it "our mother" (Galatians 4:26), and he says, "the apostle John beheld" it, referring to Revelation 21:2.
Clement of Alexandria ( 150-211 A.D.) and Origen (185-254 A.D.) also attribute John the Apostle as the author of Revelation. In his treatise, Who is the Rich man that Shall be Saved? (XLII), writes of "the apostle John" who "returned to Ephesus from the Isle of Patmos" after "the tyrant's death." The tyrant is unnamed but is believed to be Domitian.
Ignatius (30-108 A.D.) writes regarding John the Apostle,
Origen (A.D. 185-254), in De Principiis says, "According to John, God is Light" (I. II. 7), unquestionably referring to the Apostle John. Then later he says, "Listen to the manner in which John [the John whom he had quoted above] speaks in the apocalypse". (I. II. 10). Surely Origen knew only one John who wrote Scripture, and that was John the Apostle.
Hippolytus (A.D. 170-236) ; Victorinus (Died in persecution A.D. 303) as well as the Muratorian Fragment, ect. all lend their support to the genuineness of Revelation and that of being from John the Apostle of Christ. It is with great surety that such an array of testimony can lead one to accept John the Apostle as the writer of Revelation.
Eusebius (A.D. 300-340) the father of church history writes in his Ecclesiastical History about the connection between John the Apostle and Domitian.
It is said that in this persecution the apostle and evangelist John, who was still alive, was condemned to dwell on the island of Patmos in consequence of his testimony to the divine word. Irenaeus, in the fifth book of his work Against Heresies, where he discusses the number of the name of Antichrist which is given in the so-called Apocalypse of John, speaks as follows concerning him: “If it were necessary for his name to be proclaimed openly at the present time, it would have been declared by him who saw the revelation. For it was seen not long ago, but almost in our own generation, at the end of the reign of Domitian.”
Prior to the third century, there was no dispute of apostolic authorship. The bishop of Alexandria, Dionysius (200-265 A.D.), was the first to raise questions about the apostle John being the author. He claimed, based on the writing style and the lack of an apostolic claim in the book, John the Elder (Presbyter) was the author not John the apostle. Dionysius, who studied under Origen, also denied the teaching of a literal Millennium. The teaching on the Millennium was based on a literal reading of the book of Revelation (Revelation 20:1-7). The Alexandrian school taught scriptural symbolism and allegorical interpretation, rejecting a literal Millennium interpretation of Revelation. By questioning John the Apostles authorship of the book, their Amillennial view had greater credibility.
There is valuable information from the writings of Papias as brought out in Catholic Encyclopaedia:
Irenæus makes mention of these as the only works written by Papias, in the following words: Now testimony is borne to these things in writing by Papias, an ancient man, who was a hearer of John, and a friend of Polycarp, in the fourth of his books; for five books were composed by him. In the Papia-I, Papias describes his way of gathering information. This is preserved through Eusebius (III, xxix):
"I will not hesitate to add also for you to my interpretations what I formerly learned with....., but in those who relate the precepts which were given by the Lord to the faith and came down from the Truth itself. And also if any follower of the Presbyters happened to come, I would inquire for the sayings of the Presbyters, what Andrew said, or what Peter said, or what Philip or what Thomas or James or what John or Matthew or any other of the Lord's disciples, and for the things which other of the Lord's disciples, and for the things which Aristion and the Presbyter John, the disciples of the Lord, were saying. For I considered that I should not get so much advantage from matter in books as from the voice which yet lives and remains."
Here Eusebius has caused a difficulty by pointing out that two Johns are mentioned, one being distinguished by the epithet presbyter from the other who is obviously the Apostle.
Dionysius Misconception of two John:
The historian Eusebius adds that Dionysius of Alexandria said he heard there were two tombs of John at Ephesus. To quote Catholic Encyclopaedia, this view has been adopted by practically all liberal critics and by such conservatives as Lightfoot and Westcott. But Zahn and most Catholic writers agree that Dionysius was mistaken about the tomb, and that Eusebius's interpretation of Papias's words is incorrect. For he says that Papias frequently cited John the Presbyter; yet it is certain that Irenaeus, who had a great veneration for the work of Papias, took him to mean John the Apostle; and Irenaeus had personal knowledge of Asiatic tradition and could not have been ignorant of the existence of John the presbyter, if there ever was such a person in Asia. Again, Irenaeus tells us that the Apostle lived at Ephesus until the time of Trajan, that he wrote the Apocalypse in the last days of Domitian.
Irenaeus had heard Polycarp relate his reminiscences of the Apostle. Justin, who was at Ephesus about 130-5, asserts that the Apostle was the author of the Apocalypse (and therefore the head of the Asiatic Churches). But if the Apostle lived at Ephesus at so late a date, (and it cannot be doubted with any show of reason), he would naturally be the most important of Papias's witnesses. Yet if Eusebius is right, it would seem that John the Presbyter was his chief informant, and that he had no sayings of the Apostle to relate. Again, "The Presbyter" who wrote I and II Johnhas the name of John in all manuscripts, and is identified with the Apostle by Irenaeus and Clement, and is certainly (by internal evidence) the writer of the fourth Gospel, which is attributed to the Apostle by Irenaeus and all tradition. Again, Polycrates of Ephesus, in recounting the men who were the glories of Asia, has no mention of John the presbyter, but of "John, who lay upon the Lord's breast", undoubtedly meaning the Apostle. The second John at Ephesus is an unlucky conjecture of Eusebius.
Some more readings here, and here