The Brewers staff ace went to the Angels in exchange for shortstop Jean Segura and Class AA pitchers Ariel Pena and Johnny Hellweg.
Greinke has compiled a 9-3 record with a 3.44 ERA in 21 starts for Milwaukee this season. Stretching back to last year, the right-hander has won 15 straight home starts -- the longest such streak in franchise history.
He has compiled an 85-76 record with a 3.79 ERA in 259 career games, including 218 starts.
Greinke goes to a second-place Angels team that is five games behind the Texas Rangers in the American League West but is tied for the lead in the AL wild-card standings.
The key player for Milwaukee in the deal is 22-year-old Segura, who was batting .294 with seven homers and 40 RBI in 94 games for Class AA Arkansas.
Notable deaths of 2014 [PHOTOS]