The Angels announced the deal Tuesday night.
Jepsen went 3-2 with a 3.02 ERA last year, returning to an important role in the Angels' bullpen after missing much of the 2011 season with a knee injury. He has been a steady presence in Los Angeles' bullpen for the past four seasons.
Jepsen asked for $1.4 million in arbitration and was offered $975,000. He made $501,000 in 2012.
Los Angeles has settled with all its arbitration-eligible players, although third baseman Alberto Callaspo's deal is still pending a physical.