It is a two-year deal worth $2 million, a league source confirmed to ESPN.com's Ramona Shelburne. The 6-foot-10, 250-pound Davis has a player option on the second year.
With big men Pau Gasol and Chris Kaman gone, Davis figures to play a significant role for the Lakers.
Time on the court was hard to come by for Davis in Memphis last season, when he averaged 5.7 points and 4.1 rebounds in 15.2 minutes per game. He has career averages of 6.9 points and 5.9 rebounds in four seasons with Toronto and Memphis.
Davis, 25, will join Jordan Hill, Robert Sacre and rookie Julius Randle in the Lakers' frontcourt.
Yahoo! Sports earlier reported the agreement.