The club announced the decision Friday among several transactions.
Bedrosian would have been eligible for arbitration this winter.
The right-hander has spent his entire career with the Angels, who drafted him in the first round in 2010. He reached the majors in 2014 and spent seven seasons in Los Angeles' bullpen, recording a 3.70 ERA over 277 2/3 innings. Bedrosian, who has nine career saves, briefly served as the Angels' closer for two stints in 2017.
The Angels assigned catcher Jose Briceno and infielder Elliot Soto outright to Triple-A Salt Lake after they cleared waivers. Los Angeles also announced reliever Jacob Barnes had been claimed off waivers by the New York Mets. The Angels also reinstated right-hander Justin Anderson from the 60-day disabled list.