The NL Central-leading Brewers made the deal Sunday and assigned Miller to Triple-A Colorado Springs. He was cut by Tampa Bay on Thursday.
The 28-year-old Miller was hitting .256 with five home runs and 21 RBIs in 48 games for the Rays. Mostly a shortstop, he has started at every position in the majors except catcher and pitcher.
Miller hit 30 home runs for the Rays in 2016 but dipped to just nine last year.
The 27-year-old Choi hit .233 with two homers and five RBIs in 12 games for Milwaukee.
The Brewers sent Choi to Triple-A Colorado Springs earlier Sunday, one day after he hit a go-ahead, pinch-hit grand slam in the Brewers’ 12-3 win over the Phillies.