Mbah a Moute played at UCLA with Timberwolves All-Star Kevin Love, including a trip to the Final Four in the 2008 NCAA Tournament.
"We are excited to acquire a solid veteran player in Luc Mbah a Moute," said Flip Saunders, Timberwolves President of Basketball Operations. "Luc is known as one of the premier defensive players in the league with an ability to guard multiple positions. He adds a lot of energy, grit and a high basketball IQ to our team. We thank Derrick for his contributions to our organization and wish him well in Sacramento."
Williams was drafted No. 2 overall in 2011 but behind Love, there were precious few minutes for the 6-foot-8 forward. He was the highest draft pick in team history, but never adapted the game of a small forward as former general manager David Kahn envisioned.
Last month, Minnesota picked up the $6.7 million option on Williams' contract for next season.
Mbah a Moute is signed through next season and is owed $8.87 million. He was traded for the second time this year on Tuesday, going to Sacramento for two second-round picks from the Milwaukee Bucks on July 9.
Mbah a Moute was the 37th overall pick in the 2008 draft.