Belisario, who turns 31 on Dec. 31, wasn't tendered a contract on Monday by the Dodgers, the only team he's played for in his four-year Major League career.
Belisario was 5-7 with a 3.97 ERA in 77 appearances for Los Angeles in 2013, finishing second in the National League in appearances. He impressed in his rookie season in 2009 (2.04 ERA in 69 games) and again in 2012 (2.54 in 68).
He has a 3.29 ERA in 273 career games.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.