Milwaukee acquired catcher Jacob Nottingham and right-handed pitcher Bubba Derby in the deal Friday. The A's and Brewers each won only 68 games last year.
The 28-year-old Davis hit 27 home runs last season, 10th-most in the National League, and he batted .247 with 66 RBI in 121 games. Davis is not eligible for free agency until after the 2019 season.
The Brewers have acquired several young players since hiring general manager David Stearns last September. Shortstop Jean Segura and reliever Francisco Rodriguez are among the veterans Milwaukee has traded.
Nottingham, who turns 21 in April, hit .316 with 17 home runs and 82 RBI in Class A last year. He was acquired by the A's in midseason for the deal that sent Scott Kazmir to Houston -- where new Brewers general manager had been assistant GM.
Derby, who turns 22 later this month, was 1-1 with a 1.21 ERA in 14 total games at the rookie and Class A levels.
The A's also designated left-hander Sean Nolin for assignment.
Information from The Associated Press was included in this report.