The club also designated veteran right-hander Luke Gregerson for assignment before Friday's interleague game at the Texas Rangers while recalling rookie reliever Ryan Helsley from Triple-A Memphis and sending down right-hander Dominic Leone.
Martinez was a two-time All-Star as a starter for St. Louis before making 18 of his 33 appearances out of the bullpen last season. The 27-year-old is expected to be used as a reliever.
It is the second time Helsley has been brought up from the minors this season. The 24-year-old right-hander gave up two runs in 6 1/3 innings over three appearances in his first stint.
Gregerson, a 35-year-old who hadn't pitched since July until being activated May 4 coming off a right shoulder impingement, allowed five runs and 11 hits over 5 2/3 innings in six relief appearances. Leone has an ERA of 8.02 in 20 games out of the bullpen.