Los Angeles also added veteran right-handed reliever Ryan Tepera on a two-year contract.
Bradley went through his first workout with the Angels on Friday as another addition by general manager Perry Minasian to the Angels' long-struggling pitching staff.
Tepera's deal wasn't completed until Saturday, so manager Joe Maddon wasn't allowed to talk about his addition Friday. But Maddon said he was excited about the new options available to him this spring after struggles out of the bullpen throughout his tenure.
"They're really established relievers," Maddon said. "These are guys that you can count on when the score is even or you're ahead. ... It creates even more depth, because guys are going to be pushed back to the minor leagues that we feel good about, but are going to continue their process of becoming a really solid major league relief pitcher. It makes us better in the present, and it also makes us better in the future."
Bradley went 7-3 with a 3.71 ERA and 40 strikeouts last season for Philadelphia. The eight-year major league veteran has a career 3.89 ERA and experience as a starter and a closer with the Arizona Diamondbacks.
"When you look at what they've added, you really start to turn your head," Bradley said.
Bradley and Tepera were among the top free-agent relievers available, and the Angels made good on Minasian's desire to bolster a bullpen that has let down this franchise repeatedly for years. Los Angeles' relievers were 24th in the majors with a 4.59 ERA last season.
The Associated Press contributed to this report.