After playing just one season for the Clippers, Collison has a multiyear deal with the Kings that is fully guaranteed, according to NBA executives who were not authorized to speak publicly on the matter.
Collison opted out of a contract that would have paid him $1.985 million next season, looking for a bigger payday from the Clippers that never came.
"The Kings were the most aggressive team by far in the free agency, and I respected that on all levels," Collison said. "Of course, I was trying to make it work with the Clippers and tried to re-sign with them. But I didn't think they really made me their first priority like the Kings did."
With Collison's departure, the Clippers reached out to unrestricted free-agent point guard Jordan Farmar as one possible replacement.
Farmar played in just 41 games last season with the Lakers because of various injuries, averaging 10.1 points and 4.9 assists.
Rivers also reached out to free-agent small forward Luol Deng on Thursday, in hopes of looking for ways to work out a sign-and-trade deal with Cleveland, where Deng played last season.
The Clippers have available the midlevel exception, which starts at $5.3 million, and the biannual exception, a maximum deal of two years for $4.2 million.
Collison, 26, served as backup to All-Star point guard Chris Paul, but Collison was a force for the Clippers by playing in 80 games.
When Paul missed 18 games with a separated right shoulder, Collison started for him and led the Clippers to a 12-6 record, keeping them afloat in the tough Western Conference.
Collison, who went to UCLA and Etiwanda High, said he had wanted to remain with the Clippers.
"Once I understood that the Clippers had other plans, as far as trying to sign a wing player first, then I knew that the Kings were the next best option," he said. "It wasn't something that was in my back pocket. It was going to be either the Clippers or the Kings. And if you look at the Kings and what the future can have, once you put it together, we can be something really special."