The 33-year-old Loup went 6-0 with a 0.95 ERA in 65 appearances last season for the New York Mets, posting the lowest ERA among all major league relievers with at least 50 innings.
The Angels also have said they will attempt to re-sign closer Raisel Iglesias, who has emerged as likely the top reliever on the free-agent market after an outstanding sole season with Los Angeles.