Luke a physician of Antioch, as his writings indicate, was not unskilled in the Greek language. An adherent of the apostle Paul, and companion of all his journeying, he wrote a Gospel, concerning which the same Paul says, “We send with him a brother whose praise in the gospel is among all the churches” and to the Colossians “Luke the beloved physician salutes you,” and to Timothy “Luke only is with me.” He also wrote another excellent volume to which he prefixed the title Acts of the Apostles, a history which extends to the second year of Paul's sojourn at Rome, that is to the fourth year of Nero, from which we learn that the book was composed in that same city.
Therefore the Acts of Paul and Thecla and all the fable about the lion baptized by him we reckon among the apocryphal writings, for how is it possible that the inseparable companion of the apostle in his other affairs, alone should have been ignorant of this thing. Moreover Tertullian who lived near those times, mentions a certain presbyter in Asia, an adherent of the apostle Paul, who was convicted by John of having been the author of the book, and who, confessing that he did this for love of Paul, resigned his office of presbyter.
Some suppose that whenever Paul in his epistle says “according to my gospel” he means the book of Luke and that Luke not only was taught the gospel history by the apostle Paul who was not with the Lord in the flesh, but also by other apostles. This he too at the beginning of his work declares, saying “Even as they delivered unto us, which from the beginning were eyewitnesses and ministers of the word.” So he wrote the gospel as he had heard it, but composed the Acts of the apostles as he himself had seen. He was buried at Constantinople to which city, in the twentieth year of Constantius, his bones together with the remains of Andrew the apostle were transferred.
Source: De Viris Illustribus (Illustrious Men) (New Advent)