Rivers was introduced as the Clippers' new coach and senior vice president of basketball operations at a news conference Wednesday at their Playa Vista training complex.
The move was finalized Tuesday when the NBA approved the deal. Boston agreed to release Rivers in exchange for a first-round pick in 2015. Rivers went 416-305 and won the 2008 NBA title during nine seasons with the Celtics.
Boston's front office mostly had warm words for Rivers after he left for his new team.
"We don't have a championship without Doc Rivers coaching," said Danny Ainge, the Celtics' president of basketball operations. "He did an unbelievable job. He has a long history of great success with us in the last nine years, and we wish him the best in Los Angeles."
The 51-year-old Rivers is likely to be the NBA's highest-paid coach with the deal. He'll also have a prominent role in the Clippers' front office with his additional title of senior vice president.
Rivers was eagerly pursued by the Clippers, who are coming off the best regular season in franchise history with a roster built around Blake Griffin and Chris Paul.
"He felt like it was time for a change," Ainge said. "He felt like we all needed a change. That was his rationalization or justification for going to the Clippers, that this was better for everybody. I don't think there should be any resentment. I know how Boston fans are. This may be a win-win for everybody."
Rivers replaces Vinny Del Negro, who wasn't re-signed after the Clippers won a franchise-record 56 games and their first Pacific Division title last season. The Clippers will take over Rivers' Celtics contract and pay him about $7 million a year over the next three years.
The negotiations for Rivers proceeded deliberately and abruptly over the past two weeks. The Clippers also spoke to the Celtics about acquiring star forward Kevin Garnett as part of the deal, but NBA Commissioner David Stern won't allow teams to trade active players for a coach.
Rivers played one season for the Clippers in 1991-92, and they made the playoffs that season for the first time since the former Buffalo Braves moved to the West Coast in 1978. Los Angeles has made only five playoff appearances and won just two rounds since that season.
Rivers ended his playing career in 1996. He then went into broadcasting before serving as the Orlando Magic's head coach for just over four seasons from 1999-2003, going 171-168 and winning an NBA coach of the year award. He is one of four active NBA coaches who have won a championship.
The Associated Press contributed to this report.