The Acts of the apostles was written by Luke.
Luke wrote his gospel for Theophilus and begins it thus:
Luke 1:1 Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us, 2 Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word; 3 It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus, 4 That thou mightest know the certainty of those things, wherein thou hast been instructed.
The Acts of the Apostles begins was written to the same person and references the gospel as ‘the former treatise’..
Acts 1:1 The former treatise have I made, O Theophilus, of all that Jesus began both to do and teach,
Luke accompanied Paul on some of his preaching work. He joined Paul at Troas in Acts 16.
His presence is made clear when he uses the pronoun ‘we’.
Acts 16:10 And after he had seen the vision, immediately we endeavoured to go into Macedonia, assuredly gathering that the Lord had called us for to preach the gospel unto them. 11 Therefore loosing from Troas, we came with a straight course to Samothracia, and the next day to Neapolis;
Paul calls him the ‘beloved physician’ in his letter to Colossae.
Colossians 4:14 Luke, the beloved physician, and Demas, greet you.
He was with Paul when he wrote the second letter to Timothy
2 Timothy 4:11 Only Luke is with me.
I hope this helps.