Entering Sunday's game against the Pirates, Atlanta's relievers had posted a 9.11 ERA over the past 12 games.
Eveland produced a 2.63 ERA in 30 appearances with the Mets in 2014. But opponents batted .273 and compiled a .374 on-base percentage during his final 15 appearances.
The Braves began targeting Eveland after he opted out of his Minor League contract with the Red Sox earlier this week.
Eveland posted a 1.54 ERA in 16 appearances with Triple-A Pawtucket this season. He has a 5.27 ERA in 144 career appearances at the Major League level.
Mark Bowman is a reporter for MLB.com. Listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.