The 34-year-old right-hander went 9-3 with a 3.72 ERA in a career-high 65 appearances last season, earning $420,000. He requested $1.05 million in arbitration on Tuesday and was offered $850,000.
Donnelly pitched in the minors for 10 seasons before making his big league debut with the Angels in 2002. He has a 17-8 record with a 2.57 ERA and four saves in 214 appearances -- all in relief.
He earned the victory in the 2003 All-Star game, working one scoreless inning for the American League.
The Angels had seven players eligible for arbitration but reached agreements with all starting Saturday, when they announced multiyear deals with infielder-outfielder Chone Figgins and
outfielder Juan Rivera.
There are now 42 major leagues remaining in arbitration.