Morales, who broke his leg while celebrating a walk-off grand slam at home plate in late May, agreed to a $3 million, one-year deal. He was hitting .290 with 11 home runs and 39 RBI at the time.
Aybar, meanwhile, signed a one-year contract worth $3 million. After a breakout season in 2009, he struggled last year, dealing with injuries while batting .253 with five home runs and 29 RBI.
Also agreeing to one-year deals were Angels second baseman Howie Kendrick and outfielder Reggie Willits. The terms of those contracts weren't announced.
Angels ace pitcher Jered Weaver, who led the major leagues with 233 strikeouts last season, has exchanged arbitration numbers with the team, as has catcher Mike Napoli.