The Cardinals inked Motte to a one-year contract after a season in which the 29-year-old emerged as the closer for the World Champions. He set a franchise single-season record in 2011 for games pitched by a right-hander with 78, collected five post-season saves and was on the mound for the final out of the World Series.
Motte owns a 13-8 career record with 12 saves and a 2.92 earned run average.
Boston acquired Bailey in December from the Oakland Athletics, for whom he converted 24-of-26 save opportunities with a 3.24 ERA last season. The right-hander will be expected to help fill the void left by the departure of longtime Boston closer Jonathan Papelbon.
Bailey is 7-10 with a 2.07 ERA and 75 saves in 157 appearances over three major league seasons.