Terms weren't disclosed, but Rondo received a one-year deal worth $2.6 million, sources told ESPN's Adrian Wojnarowski.
Rondo, who agreed to a contract buyout with the Memphis Grizzlies on Saturday, will still make his full $7.5 million salary this season between the buyout and his new deal with the Lakers.
The two-time champion and four-time All-Star played for the Lakers for two seasons from 2018 to 2020 and was an integral piece on L.A.'s title team in the Orlando bubble.
Rondo also is joining a stable of aging All-Stars on the Lakers roster. James, Westbrook, Howard, Carmelo Anthony, Marc Gasol and Rondo were all All-Stars in 2012, the season before Anthony Davis came to the NBA.
Rondo averaged 5.4 points and 4.4 assists in 45 games with the Clippers and Atlanta Hawks last season, shooting a career-best 40.4% from 3.
He spent the first nine seasons of his NBA career with the Boston Celtics after entering the league in 2006. He has averaged 10.0 points, 8.1 assists and 4.6 rebounds over his career, which also included stops with the Dallas Mavericks, Sacramento Kings, Chicago Bulls and New Orleans Pelicans.
Information from ESPN's Dave McMenamin was used in this report.