The move freed up a roster spot for the Celtics, giving them the ability to pick up a player who gets bought out. Players must sign with a team by March 1 to be eligible for the playoffs.
Atlanta is expected to waive Bird, a second-round pick in 2017 who has not played all season because of his involvement in a domestic violence incident in September.
News of the deal was first reported by Yahoo Sports.
Bird pleaded not guilty to charges of assault and battery on a household member, assault and battery with a dangerous weapon, kidnapping, and strangulation or suffocation. Last week, he was in court on two new charges stemming from the incident. Court documents show that he told his girlfriend, "Tell anyone about this, I don't care where you are I'll find you and kill you."
The Celtics said in a statement in September that the matter would be handled by the NBA rather than the team.
Bird's next scheduled court date is Wednesday.