Thompson, 27, had a 2-6 record and a 4.84 ERA last season in 32 games including eight starts for the Cardinals.
He will not go on the 40-man roster but is expected to be invited to the Major League Spring Training camp.
In five years with the Cardinals, Thompson compiled a 21-17 record and 4.36 ERA in 185 games (32 starts). He posted his best numbers as a rookie in 2005 when he was 4-0 with a 2.95 ERA and his only big league save in 40 relief appearances.
Thompson has postseason experience including two-thirds of a scoreless inning in the 2006 World Series against Detroit. He appeared in the National League Division Series and League Championship Series in 2005 and 2006.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.