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Agent Burton Rocks said that Wells agreed to a contract with the Angels after holding a private workout for the club Friday.
Wells, 35, is 69-103 with a 4.71 ERA in 12 seasons with Pittsburgh, the Chicago White Sox and seven other clubs. He split last season between the San Diego Padres and their Triple-A Tucson club in the Pacific Coast League.
The Angels, off to a 2-8 start, rank 28th in the majors with a 5.38 team ERA and are dealing with the loss of staff ace Jered Weaver to a left elbow injury that is expected to keep him out for at least a month.
Rocks told ESPN.com that Wells's young son, Deacon, underwent open heart surgery during the offseason.
"Kip's focus was on his little boy," Rocks said in an email. "Deacon is doing well and so Kip is in full baseball mode.''