Bailey revitalized his career last season with the Angels, posting six saves with a 2.38 ERA in 12 appearances. He became Los Angeles' closer after Huston Street's season-ending injury.
The Angels are the 32-year-old Bailey's fifth big-league team. He is a two-time All-Star who won the AL's Rookie of the Year award in 2009 with Oakland, but he struggled with shoulder injuries for the previous three seasons.
To clear a roster spot, the Angels designated outfielder Shane Robinson for assignment Wednesday.