Brosseau slumped this season after hitting a huge home run for Tampa Bay in the 2020 playoffs. His tiebreaking drive in the eighth inning off Yankees closer Aroldis Chapman lifted the Rays to a 2-1 win in the decisive Game 5 of the AL Division Series.
The 27-year-old Brosseau hit .187 with five home runs and 18 RBI in 57 games for the AL East champion Rays, and also struggled at Triple-A Durham.
Brosseau is a career .245 hitter with 16 homers and 46 RBI in 143 games over three seasons, all with the Rays. The right-hander has batted .277 against lefties in his career.
Brosseau has made 50 starts at second base, 35 at third and nine at first base in the majors.
Reifert, a 22-year-old righty, made his professional debut this season, going a combined 3-3 with eight saves and a 2.10 ERA in 37 games for Low-A Carolina and High-A Wisconsin.
The trade came a couple days after the major league general managers' meetings ended.
On Thursday, the NL Central champion Brewers announced the hiring of Ozzie Timmons and Connor Dawson as hitting coaches to replace the fired Andy Haines.
Milwaukee scored a total of six runs in a four-game NL Division Series loss to the eventual World Series champion Atlanta Braves. The Brewers ranked 12th out of 30 major league teams in scoring, 20th in OPS and 27th in batting average during the regular season.