It's a one-year, $3.5-million deal, his agent told ESPN's Adrian Wojnarowski.
Cousins remains a risky option at center due to his recent injury history. However, if he's able to increase his production while staying healthy in a smaller role, the Lakers may have secured one of the steals of the offseason.
There was reportedly little market value for Boogie. The Miami Heat also had interest in signing the free-agent big man, but several Lakers players helped sway his decision to join the team after they lost out on Kawhi Leonard to the Clippers, sources told Wojnarowski.
Cousins and Rondo will play alongside Davis for the second time after the three built a strong relationship during their short stint together with the New Orleans Pelicans in 2017-18.
The 28-year-old signed a one-year deal with the Golden State Warriors last season but didn't appear in a contest until the end of January. He suffered a quad injury in Game 2 of Round 1 against the Clippers.
Cousins made a quick recovery and was able to rejoin the roster during the Warriors' NBA Finals loss to the Toronto Raptors.
Rondo, a veteran floor general, won't be tasked with scoring but will take a load off of James as an initiator.