Tavarez, who signed a deal through the remainder of the season, is expected to join the Braves for Tuesday night's game at Los Angeles.
The 35-year-old Tavarez began the season with the Boston Red Sox. He was released on May 22 and signed with Milwaukee on May 27. He was 0-2 with a 7.20 ERA in a combined 20 innings with the two teams.
Tavarez refused a minor league assignment with Milwaukee on June 25.
Tavarez has an 84-72 career record with 22 saves and a 4.46 ERA.