"Yesterday they called and said, if he can go, he can go, he's been cleared," Rivers said before Sunday's game.
Rivers said that as soon as Griffin received clearance, he jumped at the chance to return to the court.
"He just said, 'I'm ready,' " Rivers said.
Griffin has been sidelined since Feb. 8 because of a staph infection in his right elbow. He had surgery Feb. 9 to remove the infection. The Clippers have won nine of their 15 games without him.
Rivers said that Griffin does not have any minute restrictions, though he said Griffin may be limited because he hasn't played in an NBA game in five weeks.
"He's had hard rest, hard rest is when you can't condition," Rivers said. "He had three weeks or four weeks with zero conditioning. That's hard to do. And that takes awhile to get back into shape."
Griffin is averaging 22.5 points on 50.1% shooting, 7.5 rebounds and 5.1 assists a game this season for the Clippers, who are in fifth place in the Western Conference with a record of 42-24.
Reserve guard Jamal Crawford, who has missed five games with a bruised right calf, remains out.
Rivers said there's no timeline for his return. When asked if Crawford will be back before the playoffs, Rivers said he wasn't sure.
"I don't think he's improved at all, I can tell you that," Rivers said of Crawford. "That's obviously not good news."
The Clippers have 16 games remaining in the regular season.