The Falcons announced the deal Tuesday on their Twitter feed.
- Atlanta_Falcons (@Atlanta_Falcons) March 11, 2014
The Falcons also agreed with starting center Joe Hawley on a two-year deal, a source told ESPN NFL Insider Adam Caplan.
Babineaux, who turns 33 in October, was productive last season in terms of getting in the backfield, although he had just one sack to his credit. He finished the season with 49 tackles, a forced fumble and two fumble recoveries.
Babineaux still leads all defensive tackles since 2005 with 49.5 tackles for loss, according to team records.
A former second-round draft pick, Babineaux has started 108 of the 138 games he's played during nine seasons with the Falcons.
Hawley, who turns 26 in October, took over as the starting center 10 games into the 2013 season, replacing Peter Konz. He has 12 combined starts at center and right guard in 37 career games played.
ESPN NFL Insider Adam Schefter and ESPN.com Falcons reporter Vaughn McClure contributed to this report.