The deal was reported on Sunday, but will not be up for league approval until Monday, when NBA offices open. NBA commissioner David Stern said he would deny a rumored trade that involved Rivers' contract and player Kevin Garnett as a package deal.
The Clippers and Celtics are confident that this trade will put Rivers in L.A.
"This is very, very close to being done," said an official, who is not authorized to speak on the trade. "The belief with both teams is that the deal is going to get there."
Donald Sterling, owner of the Clippers, is working to finalize a contract that would pay Rivers $6 million to $7 million per season as part of a five-year deal.
Rivers currently has three years and $21 million on his contract with the Celtics.