The Acts of the Apostles was written by Luke, a physician and companion of the Apostle Paul. This is established by the opening of Acts, where the author addresses the same recipient, Theophilus, as in the Gospel of Luke (compare Luke 1:1-4 with Acts 1:1-2). Acts 1:1 refers to "my former book" (the Gospel of Luke), making it clear that both works share the same author.
Luke is also identified as the author through the "we" passages in Acts (such as Acts 16:10-17, 20:5-15, 27:1-28:16), where the narrative shifts to first-person plural, indicating the author was personally present with Paul during portions of his missionary journeys. Early church tradition unanimously attributes both the Gospel of Luke and Acts to Luke.
Paul, while the central figure in much of Acts, was not its author; he wrote the epistles (letters) that bear his name. Matthew wrote the Gospel of Matthew. Peter wrote the epistles of 1 and 2 Peter. None of these figures authored Acts.