Tampa Bay will send Milwaukee $2,209,677 as part of the trade, which will offset all but $500,000 of the $2,709,677 remaining in Miller's $4.5 million salary this year.
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.
"At this point we thought that the positional versatility and the infield experience that Miller brings would be helpful," Brewers general manager David Stearns said, according to the Journal Sentinel. "He will head to Triple A, and when we have a need, I'm sure he will be ready to contribute."
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 2 homers and 5 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.
The Associated Press contributed to this report.