Rauch was just 1-2 with a 7.56 ERA in 15 appearances for the Marlins last season, but the 35-year-old right-hander was 3-7 with a respectable 3.59 ERA with the Mets in 2012.
The 6-foot-11, 290-pound Rauch will have to win a spot in a loaded Royals bullpen in spring training. Kansas City returns intact one of the American League's best relief corps.
Rauch is 43-40 with a 3.90 ERA over 11 major league seasons. His best seasons were with the Twins from 2009-10, when he was 8-2 with a 2.82 ERA in 76 appearances.