It is apparent from the prologue of Acts that its author is the same as that for what we refer to as the “Gospel According to Luke!” Both were written about the Lordship of Jesus and the Kingdom of God (Acts 1:3; cp. Luke 4:43) to someone by the name of Theophilus. Moreover, Acts refers Theophilus to his former treatise or account (logos – G3056) concerning all that Jesus began to both do and teach (Acts 1:1; cp. Luke 1:3). Many modern critics try to tell us that, because neither work is signed that we cannot know the author of either.
One thing seems certain; if we know the author of either work, we will have found the author of both. Tradition tells us the name of the author is Luke, but is this accurate? Is it possible to find out with relative certainty who the author might be for both works? Yes, I do think there is enough evidence in antiquity that would point to our author. To whom do the earliest witnesses point as the author of both the Gospel of Luke and the Book of Acts?
Luke also, the companion of Paul, set down in a book the gospel preached by him. (Irenaeus, Against Heresies 3:1:1; cir. 180 AD)
The Acts of the Apostles, however, were written by Luke in one book addressed to the most excellent Theophilus; and he makes it clear that these events took place in his presence, for he omits the passion of Peter, as also the journey of Paul when he went from the city to Spain. (Muratorian Fragment, A.D. 200
These two witness show that the author of both works were believed to have been written by a man named Luke. Both Irenaeus and the Muratorian Fragment tell us that Luke was a companion of Paul, and both witnesses come down to us in less than 200 years after the works were written. Furthermore, that the author of both works was a companion of Paul’s is acknowledged in the Book of Acts, itself, through what have become known as the “we” passages. For example, in Acts 16 we find Luke saying of Paul’s missionary group: “And they passing by Mysia came down to Troas” (v.8). It is in Troas that Paul seems to link up with the author of Acts, because he says “…the Lord had called us…” (v.10) and then “Loosing from Troas, we came… to Samothracia” (v.11). There are more such passages in Acts 16 and also in chapters 20, 21, 27 and 28. So, we are able to conclude from Scripture that the author of Acts was indeed a companion of Paul.
Scripture doesn’t tell us very much about Luke. There are only three passages in the New Testament that specifically refer to a man by the name of Luke (G3065), and it does seem as though he was a companion of Paul. Colossians 4:14 says he was a beloved physician and names him among two gentiles (Colossians 4:12-14) over against Paul’s kinsmen mentioned in Colossians 4:11. So, this Luke appears to be a gentile. The other places in Scripture where the name Luke is mentioned is 2Timothy 4:11 where Paul writes that only Luke is with him; and Philemon 1:24 where Lucas (G3065) is mentioned as Paul’s fellow-laborer. The problem is that, although Luke is mentioned as a fellow-laborer, it is not specifically stated he labored in the word. Some of Paul’s fellow-laborers worked in the marketplace to support Paul’s fulltime ministry (see Epaphroditus in Philippians 2:25-26; cp. 3John 1:8). At least at times this phrase largely refers to that person or those people ministering to Paul’s needs as he preaches the Gospel. When he had no such fellow-laborers, he worked with his own hands to both support himself and his ministry.
Another candidate for Luke, the Gospel writer, is Lucius in Acts 13:1. He is listed among the prophets in Antioch, and it is implied in Acts 11:20 that he was one of the original evangelists who founded the gentile church there. Lucius (G3066) and Lucus (G3065) are derived from the same root. They are essentially the same name. Saul was Paul’s name as a Jew, but he changed it to Paul later in Acts 13 (more about this when we come to that part of Acts). Paul is a Latin name and he used it among the gentiles. People often went by more than one name in ancient times. Many of the Apostles had different names by which they were known. The point is: Lucius (Acts 13:1) was definitely given the gift of evangelism and was listed as one of the prophets and one of the leaders of the church at Antioch. Luke, the physician (if he is not the same person as Lucius) is never explicitly described as a laborer in the word of God. Elsewhere, we find Lucius listed among those at the Corinthian church (called Chenchrea in Romans 16:1) with Paul (Romans 16:21) where Paul wrote the Epistle to the Romans. The city of Corinth had two harbors—one bordering westward on the Adriatic Sea and the other (Chenchrea) eastward, bordering on the Aegean Sea. Paul founded the Church of Corinth in the Chenchrea district.
In 2Corinthians 8:16-18 Paul’s letter is brought to Corinth by Titus and someone Paul describes as “the brother whose praise is in the Gospel throughout all the churches.” Who might this be? Certainly Titus labored in the Gospel, but he is not the one described in this manner. Furthermore, it is presumed that this description alone would identify this man. I suggest that it is the writer of the Gospel of Luke and Acts. When Paul finally comes to Corinth to winter there (1Corinthians 16:6; cp. 2Corinthians 1:15-16 & 2:1) and from where he wrote the Epistle to the Romans, we find Lucius, not Luke mentioned with him at Corinth (Romans 16:21). So, it seems that the one travelling with Paul at this point and to whom the “we” passages of Acts 20, 21, 27 and 28 refer is Lucius. The name Luke is not mentioned as being with Paul at Corinth. If he is there and Paul doesn’t mention him, it would be a glaring oversight! That simply would not be done. Understanding this, if Luke (the beloved physician, a gentile) is not with Paul in Corinth at this time, he cannot be referred to in those “we” passages that show him to be the writer of Acts. Therefore, Lucius, the Messianic Jewish evangelist and co-founder of the Antioch church, must be the Luke to whom the 2nd and 3rd century church fathers refer.
 This idea would fit the context of the Bible being written by Israelites. If Luke is a full blooded gentile as Colossians 4:14 implies the “beloved physician” is, then this would be the ONLY gentile who wrote anything in the whole Bible, and this without any introduction or logical support. Moreover, Luke and Acts show insider Jewish information that we would expect only a Jew to know and understand. Like the priestly course of Abjah (Abia) in Luke 1:5; the subtle reference to the high priestly robes in Jesus’ rabbinical story of Lazarus and the rich man, and his reference to the rabbinical hope of coming to the bosom of Abraham in the same story, something a Christian gentile would not be expected to know—our hope is in Christ, not Abraham! In Acts 1:9 we find the Ascension of Jesus described in a manner that subtly refers to Daniel’s ascension of the Messiah to his throne in Daniel 7. In Acts 4:34 we see the Messianic Jews living as though they had no debts, a fulfillment of the sabbatical year described in Deuteronomy 15:1-4. An ordinary gentile with no Jewish background before becoming a Christian would not be expected to know Jewish things like this.