The deal includes future team options that give the Celtics an ability to keep Babb beyond this season, sources said.
Babb completed his second consecutive 10-day contract with Boston on Thursday.
Babb's agent, Greg Lawrence of Wasserman Media Group, confirmed to Yahoo Sports that an agreement had been reached.
Since Avery Bradley returned from injury for the Celtics, Babb has gone four straight games without playing. After finishing his career at Iowa State, Babb averaged 12 points, six rebounds and four assists for the Maine Red Claws of the NBA Development League.
The Celtics have been most pleased with Babb's tenacity on the defensive end.