Given this evidence, the author of the book of Acts, though unnamed, can be determined to be most likely Luke. There appear three sections in which the first person plural is used. Starting in Troas,  leaving off and taking up again at Philippi,  and finally the trip to Rome . Of Paul's named companions only Luke and Titus could have been the author. Since only Luke was with him in prison right before his death, this eliminates Titus.
Since the introduction to the Acts clearly states that it is a volume to complete the Gospel account (both to Theophilus), it can be concluded that both books were written by a meticulous historian, the physician with a scientific eye for detail and accuracy.
Not an eyewitness to the life and ministry of Jesus, Luke conducted interviews and collected information to verify the stories that had been circulating in the generation since the Resurrection. Since he joined Paul in Troas,  it can be assumed he had become a believer sometime before that. That he is writing to a Roman official indicates that the Gospel is a defense of the message being preached in Acts. It could very well have been a defense treatise for his friend Paul.
On learning of Paul's vision to cross over into Macedonia, Luke joined the team. He was there when Lydia and the ladies by the river came to believe the Gospel, as well as when Paul cast out a demon from a young girl there in Philippi. He heard Paul's report of the imprisonment there as well.