Last month, Clippers All-Star point guard Chris Paul said it would be "unacceptable" if Donald Sterling still owned the team when the 2014-15 season began. Rivers, meanwhile, had said he wouldn't want to continue as the Clippers' coach if Sterling remained in that position.
Rivers called Tuesday "an amazing new day in Clippers history."
"I couldn't be more excited to work together with Steve as we continue to build a first-class, championship organization," he said in a statement released by the team. "I am already inspired by Steve's passion for the game, his love of competition and desire to win the right way, and I know our players and fans are going to be inspired as well."
Paul and several other players concurred.
"I am very excited about Mr. Ballmer's purchase of the Clippers," Paul said. "I've had a chance to meet him, and his excitement for the game of basketball and our team is going to be great for the league, the city of Los Angeles and Clipper fans everywhere."
Added All-Star forward Blake Griffin: "Today is a great day for the Clipper organization and fans everywhere. I look forward to having Mr. Ballmer as an owner and continuing our pursuit of a championship."
Information from ESPN's Darren Rovell and Jeff Goodman and ESPNLosAngeles.com's Arash Markazi was used in this report.