Blevins signed a $1.5 million minor league deal with Oakland in February but spent the start of this season at Triple-A Las Vegas, where he had a 1.69 ERA in seven games.
The Braves selected Blevins' contract from Triple-A Gwinnett and added him to their active roster before Sunday's game against the Colorado Rockies. Right-hander Wes Parsons was optioned to Gwinnett and closer Arodys Vizcaino (shoulder) was transferred to the 60-day injured list in corresponding moves.
Blevins, 35, had a 4.85 ERA in 64 appearances last season with the New York Mets. The 13-year veteran was much better in the previous two seasons with the Mets, posting a 2.87 ERA over 148 combined appearances in 2016 and 2017. He has a 3.52 career ERA in 12 seasons with Oakland, Washington and the Mets.
Atlanta hopes Blevins will help a bullpen that entered Sunday with a 4.74 ERA and a league-leading 62 walks in 26 games.
Information from The Associated Press was used in this report.