Downs went 5-5 with a 2.64 ERA in 67 appearances last year with the Blue Jays. He recorded a club record 26 holds -- third-best in the American League.
In 2007, Downs led the AL with 81 appearances and tallied a 2.17 ERA.
The Angels further bolstered their bullpen by signing reliever Hisanori Takahashi. The left-hander went 10-6 with a 3.61 ERA last year with the Mets.