Atlanta acquired White from Milwaukee on Tuesday in exchange for cash.
The 31-year-old White had produced at an above-league-average level for Triple-A Nashville this season (.788 OPS, 113 wRC+), but the Brewers were presumably keen on opening up playing time at their top minor-league affiliate for younger players. White will fill a similar organizational depth role for Atlanta, with any potential call-up to the majors likely to hinge on the team losing any of its first-base or designated-hitter options to injuries over the final six weeks of the season.