The Cardinals selected McGreevy's contract from Triple-A Memphis on Wednesday.
McGreevy will start Wednesday's series finale against the Rangers in what will be his major-league debut. The right-hander has put up pedestrian numbers at Memphis this season, collecting a 4.45 ERA and 96:36 K:BB over 109.1 innings. He's been at his best over the last two months, though, with a 2.94 ERA and 52:19 K:BB across 52 frames since June 1. McGreevy is expected to be sent back down to Memphis after the spot start.