Terms of the contract were not disclosed. He will wear uniform No. 12, the team said.
Davis, 28, reached a buyout with the Orlando Magic on Friday and was waived. The Brooklyn Nets had also shown interest in Davis, but decided to sign Jason Collins, feeling that they were out of the running on Davis.
Davis, averaging 12.1 points and 6.3 rebounds in 45 games this season, was making $6 million this season and was due to make about $6.6 million next season.
Clippers coach Doc Rivers was hoping to sign Davis, who played for Rivers with the Boston Celtics from 2007 to 2011, winning a championship in 2008. Davis would be the only player on the Clippers roster to have won an NBA title.
"It's not official yet but hopefully it will be," Rivers said Sunday. "It gives us another big and what I like about a guy like that is he can play a five with a four. If we got a guy like that, he also knows my system."
Rivers was coy but smiled when asked about Davis possibly joining the team as early as Monday.
"I've heard of him," Rivers said Sunday when asked about Davis. "We call him Baby Baby. ... Whatever happens happens soon. I have a hunch. I do have a hunch but until everything is done I have no idea."
After deciding not to extend Sasha Vujacic's 10-day contract and trading Antawn Jamison and Byron Mullens, the Clippers roster currently stands at 12. The roster flexibility was created in part to give the Clippers the opportunity to sign players like Davis who were bought out.
"The one thing we did predict right was the buyout season would be active this year and I don't think it's finished," Rivers said. "I think there will be more guys being bought out. It's every man for themselves right now I guess."