Bradley, 30, hit a career-high .283 with seven home runs and 22 RBIs in 55 games last season for the Boston Red Sox.
The 2016 All-Star owns a .239 career average with 98 home runs and 60 stolen bases in 873 games during his eight-year MLB tenure.
The Gold Glove center fielder was a first-round pick by the Red Sox in the 2011 MLB Draft. He made his MLB debut in 2013. He went on to win an ALCS MVP Award and the 2018 World Series with Boston.
Christian Yelich is expected to be the Brewers' everyday left fielder this season. Bradley, Lorenzo Cain and Avisail Garcia are likely to fill in at center field and right field.
The Brewers face the Cleveland Indians in a spring training game at 3:10 p.m. EST Thursday at American Family Fields of Phoenix.