Bedard had been in the running for the No. 5 spot in the Rays' rotation, a job that manager Joe Maddon ultimately gave to top prospect Jake Odorizzi on Saturday.
Bedard had an opt-out clause in his contract that would have kicked in March 31. He said last week that he would use the clause if he failed to make the Rays' rotation.
Bedard, 35, had a 6.88 ERA and 1.82 WHIP in 17.0 innings this spring for Tampa Bay.