Luke writes his Gospel and the Acts
Luke 1:1–4; Acts 1:1–3; Colossians 4:14
Luke, the beloved physician and Paul's traveling companion, wrote an orderly account in two volumes for Theophilus: the life of Jesus and the spread of the gospel from Jerusalem to Rome.
it seemed good to me also, having traced the course of all things accurately from the first, to write to you in order, most excellent Theophilus; that you might know the certainty concerning the things in which you were instructed.
Luke 1:3–4 (World English Bible)
Luke says he carefully investigated everything from the beginning, using eyewitness sources, so that Theophilus might know the certainty of what he had been taught. His careful details of Roman officials, titles, and places have repeatedly been confirmed by archaeology. Acts ends with Paul under house arrest in Rome, which suggests to many that it was finished then.
Dating notes
If Acts was written when its story ends, about AD 62, the Gospel came shortly before. Many scholars prefer AD 70–90. The date is an estimate; Scripture doesn't say when the book was written.