Terms of the deal were not announced Thursday, but league sources previously told ESPN's Adrian Wojnarowski that Mbah a Moute's deal is for one year and $4.3 million.
A 31-year-old forward, Mbah a Moute averaged 7.5 points, 3.0 rebounds and 1.18 steals in 61 games for Houston last season.
He played two seasons for the Clippers from 2015-17, averaging 4.6 points and 2.2 rebounds in 155 games, including 137 starts.
Mbah a Moute was selected 37th overall by Milwaukee in 2008 after three seasons at UCLA. Besides the Clippers and Rockets, Mbah a Moute has played 10 seasons with Milwaukee, Sacramento, Minnesota and Philadelphia.
The Associated Press contributed to this report.