Gregerson, a reliever, was 7-6 with 10 saves and a 3.35 ERA last season in 57 games for Double-A Springfield. He had 78 strikeouts in 75 1/3 innings.
Gregerson is the player to be named in the December deal that sent right-hander Mark Worrell to San Diego for Greene. Worrell recently discovered that he needs Tommy John elbow ligament replacement surgery and will miss the entire 2009 season.
Gregerson was a 28th-round selection by the Cardinals in the 2006 First-Year Player Draft. In three seasons and 138 relief outings, he's 16-12 with 48 saves, a 2.72 ERA and 195 strikeouts and 61 walks in 172 1/3 innings.
Gregerson, 24, will report to the Padres' Major League camp on Tuesday. Greene was sent to the Cardinals on Dec. 4.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.