Downs, 34, went 5-5 with a 2.64 ERA in 67 games for the Toronto Blue Jays last year.
The Angels emerged from the winter meetings this week without their top target, outfielder Carl Crawford, who agreed to a seven-year, $142 million deal with the Boston Red Sox. Their two offseason acquisitions have both been left-handed relievers. They signed Hisanori Takahashi to a two-year, $8 million deal earlier this month.
A nine-year veteran, Downs is 27-28 with a 3.79 ERA in his career.
The Angels' priority now moves to improving the offense. They finished second in the major leagues in runs scored in 2009, but slipped to No. 19 last season.
They likely will cast a wide net, though Friday's signing could signal a continued hesitation to do business with agent Scott Boras, who represents Soriano. Another Boras client is third baseman Adrian Beltre, the top position player left in free agency.
"Right now, we're very satisfied with the starting pitching we have and with the bullpen we have. Now, it's on to see what other opportunities come up," Angels general manager Tony Reagins said.
Manager Mike Scioscia has often had bullpens without a left-hander, including last season, but Reagins said he isn't looking to inject Takahashi into the starting rotation and trade one of the Angels' starters. Scioscia said Downs will be among a mix of relievers, including Fernando Rodney, Kevin Jepsen and Jordan Walden, who could close games. The Angels have now spent $23 million on middle relievers this offseason.
"If we need one or two guys at times to get the last out, we're going to do it but I don't think the committee's going to be very large," Scioscia said.
The signing of Downs makes it unlikely the Angels will pursue closer Rafael Soriano.
Mark Saxon covers the Angels for ESPNLosAngeles.com.