Grilli, a right-hander, last pitched for the Rangers in 2009. He signed a minor-league deal with the Indians prior to last season before suffering a knee injury that cost him all of the 2010 campaign.
Grilli's best season in the Majors (3.00 ERA) came in 2008, when he split time with the Tigers and Rockies. For his career, he has a 4.74 ERA over 356 2/3 innings.
Grilli, 34, is a former first-round pick of the Giants and has pitched for five teams.