The moves were announced on Sunday before the Marlins' game against the Pittsburgh Pirates. Donnelly was active for the game and will pitch out of the bullpen.
Donnelly, who turned 38 on Saturday, was originally signed by the Chicago White Sox in 1992. He started his major league career with the Anaheim Angels in 2002. He pitched for Boston in 2007 and Cleveland in 2008. He won World Series titles with the Angels (2003) and the Red Sox (2007).
He is 26-9 with a 3.12 ERA with four saves in 318 appearances. He opted out of a contract with the Houston Astros earlier this season.