In the book of Acts, we see this call was directly Jesus Christ appearing to him supernaturally and calling him to be an apostle. He didn't make this decision, "Hey, I'd like to be an apostle. I'm going to go out and start preaching to churches and traveling around." No. Jesus called him to be this. So this is where his authority comes from as an apostle. Jesus in Acts 9, he told Ananias, Ananias was the brother who Jesus said, "You go and find Paul," and he tells him to baptize him.
He says, "Paul, he's the one who's persecuting us." And Jesus says this, "Go, for he is a chosen instrument of mine to carry my name before the Gentiles and kings and the children of Israel."