CBSSports.com reported that Myers' deal includes a club option for 2014. Terms of the agreement weren't immediately available.
Myers, 32, is 97-93 with a 4.20 ERA in 11 seasons with Philadelphia, Houston and the Chicago White Sox. He has pitched as both a starter and a reliever in the big leagues, but is expected to slot into the Cleveland rotation in 2013.
Terry Francona, Cleveland's new manager, was managing the Phillies in 1999 when they selected Myers with their first-round pick in the first-year player draft.