The Clippers said Davis will take a required physical exam Tuesday and should play Wednesday at home against the Houston Rockets.
"We were on the phone with him and just told him what we offered and I'm sure the other guys did that," Clippers coach Doc Rivers said. "I do think that it helped a little bit that we have a relationship. He knows me and I know him. I think that's the situation he wanted to be in and that's good."
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.
"I just really felt the Clippers were heading in the right direction," Davis said. "They're young, they got a great coach, a great point guard, a great rising star like Blake Griffin and DeAndre Jordan and guys that you can build around and I feel like I'm one of those types of guys, a glue guy."
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.
Rivers said he would continue following the buyout market this week with the Clippers having two roster spots available to fill.
"We're tracking the market," Rivers said. "It just keeps changing really it seems like every day more and more guys are getting bought out probably even more than I thought would happen. If we can improve our team, we would like to."