"Andre Drummond gives us powerful, anchor-point skills on both ends of the court," Lakers general manager Rob Pelinka said in a statement Sunday.
"We feel extremely fortunate to add a player of his caliber and magnitude to our core group at this stage of our journey to defend the NBA title."
The Lakers did not disclose the terms of the deal.
Drummond, 27, averaged 17.5 points, 13.5 rebounds and 2.6 assists per game in 25 appearances this season for the Cleveland Cavaliers. He has averaged 14.6 points and 13.8 rebounds per game in nine seasons.
The Cavaliers and the two-time All-Star agreed to a contract buyout last week and Drummond cleared waivers Sunday.
The four-time NBA rebounding champion entered the league as the No. 9 overall pick by the Detroit Pistons in the 2012 NBA Draft. The Pistons traded Drummond to the Cavaliers in February 2020.
The Lakers (30-17) next host the Milwaukee Bucks at 10 p.m. EDT Wednesday at Staples Center in Los Angeles.