After earlier negotiations to send Rivers to Los Angeles broke down over league objections, the deal has been revived and is pending NBA approval, unnamed sources told the broadcaster.
The report said Rivers has agreed to a three-year, $21 million contract with the Clippers. The Celtics will receive a 2015 first-round pick as compensation.
Boston has reportedly agreed to release the nine-year coach from the remaining three years and $21 million on his current contract.
The deal for Rivers is believed to help clinch a deal to retain pending free-agent all-star guard Chris Paul on a long-term contract.
Boston's initial efforts to send both Rivers and Celtics forward Kevin Garnett to the Clippers were met with resistance from NBA Commissioner David Stern, who determined they violated league rules, the sources said.
As a result, any further efforts to trade Garnett are reportedly on hold.
The Celtics have scheduled a Monday news conference with Rivers to discuss the deal, ESPN said.