The Rays sent Smith to the Braves in exchange for cash considerations, according to the team. Atlanta also activated left-hander Grant Dayton from the 10-day injured list Wednesday and designated catcher Jeff Mathis for assignment.
Smith was designated for assignment by the Rays on Sunday. He was 1-for-4 in just three games for Tampa Bay this season.
Mathis, 38, was 0-for-9 with five strikeouts in three games for the Braves this season.
Also Wednesday, the Braves optioned left-hander Tucker Davidson to Triple-A Gwinnett in a corresponding roster move after Dayton was activated from the injured list. Dayton was recovering from thigh inflammation.
Davidson allowed three runs in six innings against the New York Mets on Tuesday night in his 2021 debut.