Heidegger's Bible Handbook: Acts: Authorship

3. The writer of the book was Luke.

That the author of the book is Luke the Evangelist, the same who also wrote the Gospel, is today generally agreed among all. Although Saint Chrysostom relates that in his own time it was doubted by some. That the author of the Gospel and of Acts is certainly one and the same person, the writer of this book sets forth by a clear indication, thus writing at the beginning: In the volume above, we spoke, O Theophilus, concerning all things that Jesus began both to do and to teach, until the day in which He was taken up again, Acts 1:1, 2. Therefore, whoever wrote to Theophilus about the teaching and acts of Christ, the same consigned the Acts of the Apostles to writing. But, that Luke did that, the beginning of his Gospel indicates. Saint Jerome commends this book on account of its author: The Acts of the Apostles appears to express a bare history, and to weave together the infancy of the nascent Church. But, if we know that the writer of those things was Luke the physician, whose praise was in the Gospel, we would likewise observe that observe that all his words are medicine for the sick soul.[1]

[1]Epistle 53.

Dr. Dilday's Lecture: "Acts of the Apostles, Part 2"