Farnsworth had 25 saves and a 2.18 ERA for the Rays in 2011, both career bests, but has mostly struggled since. He began last season on the disabled list with a strained right elbow and was relegated to middle relief when he returned, going 1-6 with a 4.00 ERA in 27 innings.
The Rays had trouble finding work for Farnsworth this season, and the 37-year-old right-hander was not very effective when called upon. In 29 2/3 innings over 39 appearances, he put together a 5.76 ERA and 1.48 WHIP, with only 19 strikeouts.
Farnsworth, who was signed for $1.25 million for 2013, would have been a free agent following the season.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.