Perez gave up eight runs in 1 2-3 innings in the Braves' 15-4 loss to the Yankees on Friday night. He had a 5.56 ERA in 17 games with Atlanta.
Brigham was 0-1 with a 4.80 ERA in 11 games, all in relief, in an earlier stint with the Braves. He is a combined 9-4 with a 3.50 ERA with Double-A Mississippi and Gwinnett this season.
The Braves announced the moves before Saturday night's game against New York. It was not immediately known if the 27-year-old Brigham will move into Perez's spot in the rotation.