Downs has been a bright spot on an otherwise struggling Angels team this season, going 2-3 with a 1.84 ERA in 43 games. The left-hander's streak of 29 consecutive scoreless appearances was snapped last week.
In exchange, the Angels obtained relief pitcher Cory Rasmus.
Rasmus, 25-year-old right-hander, is a former first-round Braves draft pick. He has made three relief appearances for Atlanta this year while posting a 1.72 ERA in 37 games with Class AAA Gwinnett this season.
The hurler is the younger brother of Toronto Blue Jays center fielder Colby Rasmus.