The Cavaliers announced the deal Thursday, three hours before the NBA's trade deadline.
"We're excited about the future here," coach Byron Scott said.
The deal saves the Clippers considerable money the next two seasons while giving them a younger point guard who made the All-Star team while playing with LeBron James.
Davis is still owed nearly $28 million over the next two seasons and the balance of his $13 million contract this year. Moon's contract expires after this season. Williams is owed the balance of his $9.3 million salary this season and, with player options of $8.5 million for each of the next two years, potentially could get out of his contract altogether. The savings should give the Clippers more flexibility in free agency the next two seasons.
The Clippers would give up a likely top-10 lottery pick to make the savings happen.
"The drill is, as always, is 'Is the player you're getting back more valuable than the potential you could get in the draft?'" said Clippers general manager Neil Olshey. "Our analysis at this point in February is that it was more valuable to get a 28-year-old All-Star point guard that we have for the next few years, cap flexibility to make sure we take care of business and re-sign DeAndre Jordan and have flexibility to take care of Eric Gordon as well, as opposed to speculating on another kid that's 19 years old with one year of college experience.
"And I'm not that high on the draft to begin with this year."
But the lottery pick from the Clippers was exactly what the Cavs were after. A Cavs source told ESPN.com that the trade was made primarily for the draft pick.
"We know we're going to have to build this team through the lottery," the source said. "We hope Baron works out, but our primary focus was the pick. We really wanted two top-10 picks to infuse the team with young talent."
In Davis, the Cavs get a veteran who, when he's engaged, is one of the top point guards in the league. But will Davis be engaged on a team with the worst record in the NBA?
"Baron won't be happy," a general manager who has had past dealings with Davis said Thursday before the trade became official. "This is a worst-case scenario for him. He was just starting to get happy in L.A. playing with [Clippers rookie] Blake Griffin. There's not much to get excited about in Cleveland these days."
Griffin reacted to the news via Twitter, saying on his account: "Definitely gonna miss playing with the big homie @Baron_Davis but wish him nothing but success and health."
"Look, Blake really likes Baron," Olshey said Thursday. "But Blake also knows that we're in it with him and Eric for the long haul and he knows we've gotta do what's right for the organization and he trusts both [coach] Vinny [Del Negro] and myself that we're gonna put the right pieces around him. I can tell you that the first thought process at any point when we start to do a deal is, 'How is this going to affect Blake and Eric?'
"And we felt like this is really going to help Eric on both sides of the ball and with Blake, we really felt like it's going to free him up."
The trade revived discussions that began over the summer, when the Cavaliers scrambled to upgrade their talent to appease James, but those talks ultimately collapsed when Clippers owner Donald Sterling nixed the deal.
Williams is getting another fresh start. Acquired by the Cavs before the 2008 season from Milwaukee, Williams was deeply troubled by James' decision to leave. He's battled injuries all season, but the Clippers are confident he can make them better.
"Mo has experience where he can control the game for us and get guys in the right spots," said Del Negro. "He's been in big games, he's a very good free throw shooter and he makes big shots. And that's what we needed. He was the right fit for us."
Neither Davis nor Williams suited up Wednesday night. Davis sat out the Clippers' loss to the New Orleans Hornets with swelling in his knee. Williams sat out Cleveland's loss to Houston, after returning from a hip injury before the All-Star break.
In Cleveland, the 31-year-old Davis will be reunited with Scott. The two clashed repeatedly during their time together in New Orleans, but Scott said they fixed their relationship last summer.
Scott said Davis approached him before a preseason game and apologized for his past behavior.
"He hugged me and said, 'I love you,'" Scott said. "It's water under the bridge. We let it go."
Scott said he was moved by Davis' gesture.
"I was very touched," he said, "to the point that I was speechless. From that point on, our relationship has been very good."
There also is a question of how the trade would affect Griffin, who seemed to be developing a chemistry with Davis.
"I think anything's possible," said a source with knowledge of the talks. "I mean, would Utah really trade Deron Williams?"
Before the deal was officially complete, Williams reached out to Cleveland fans on his Twitter account.
"I wanna say thank you to all Cavs fans," he wrote on mogotti2. "It's been great. We've had some really good yrs and memories. I will never forget u guys."
Olshey and Del Negro are scheduled to take Williams and Moon out to dinner in Los Angeles on Thursday night to map out their plan for the remaining 24 games.
In a separate move Thursday, the Cavaliers acquired rookie center Semih Erden and forward Luke Harangody from the Celtics for a 2013 second-round draft pick. The Cavaliers waived veteran forward Leon Powe to make roster room after the two deadline trades.
Ramona Shelburne is a reporter and columnist for ESPNLosAngeles.com. Chad Ford is an NBA Insider for ESPN.com. Information from ESPNLosAngeles.com's Pedro Moura and The Associated Press was used in this report.