In a pair of corresponding moves, the Angels designated right-hander Luis Madero for assignment while Adalberto Mejia cleared waivers and was released.
Andriese, 30, made 54 appearances out of the bullpen for the D-Backs last year, posting a 4.71 ERA and 3.72 FIP. He owns a 4.64 ERA in 49 starts and a 4.50 ERA in 118 relief appearances.
Following the trade, Angels general manager Billy Eppler stated that Andriese will compete for a rotation spot in spring training, according to Mike DiGiovanna of the Los Angeles Times.
The right-hander is entering his second year of arbitration and won't be eligible for free agency until after the 2021 season.
Beasley, meanwhile, is a 24-year-old right-hander who made it to Triple-A Salt Lake this past season after one-and-a-half years at Double-A. In three starts, he struggled to the tune of a 7.90 ERA and 4.38 FIP.