Davis will hold the option on his 2015-16 contract, a source said.
Davis has the chance to earn considerable minutes with the Lakers, who also drafted power forward Julius Randle out of Kentucky in June.
Davis, who is 6-foot-10 and 230 pounds, has shown flashes throughout his career. Nevertheless, he likely needed a change of venue after a year of political infighting within ownership, management and the coaching staff complicated his role in Memphis last season.
Davis, 25, averaged 5.7 points and 4.1 rebounds in 15 minutes per game last season. The Toronto Raptors made him the 13th overall pick in the 2010 NBA draft.
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