Moylan, 39, tied for the American League lead with 79 appearances last season for the Kansas City Royals and had a 3.49 ERA in 59⅓ innings.
The right-hander has pitched eight of his 11 major league seasons with the Braves but spent the past two seasons with the Royals. He also pitched for the Los Angeles Dodgers in 2013.
In 460 career appearances, Moylan is 24-9 with four saves and a 3.00 ERA in 390⅓ innings.
To make room for Moylan, the Braves designated right-hander Mauricio Cabrera for assignment.