Thompson's contract was selected from Triple-A Memphis on Friday.
Thompson is one of the Cardinals' top prospects, and the team has spent the last two years developing him as a starter in Memphis. He's made 10 minor-league starts this year and has posted a 4.67 ERA and 1.16 WHIP in 44.1 innings. The southpaw hasn't yet made his major-league debut but will join the active roster for the first time in his career. The Cardinals have a doubleheader against the Cubs on Saturday, but it's not yet clear whether Thompson will make his big-league debut as a starter or out of the bullpen.