This should give the Lakers the frontcourt help they need.
Gasol is certain to help a Lakers team reeling from a series of recent injuries to inside players, including blossoming center Andrew Bynum.
Gasol, averaging 18.9 points and 8.8 rebounds in 39 games this season, can fill in at center until Bynum returns in mid-March and then move to power forward.
The Grizzlies also will get guard Aaron McKie, signed earlier Friday for salary cap purposes, and the rights to Gasol's brother Marc, a former second-round pick of Los Angeles.
The Lakers also receive the Grizzlies' second-round pick in 2010.
"We're extremely pleased to be able to make this trade," Lakers general manager Mitch Kupchak said in a statement. "Pau is a proven player of All-Star caliber in this league who can score and rebound and is still a young player. We feel this strengthens our team in the short term as well as the long term."
The Lakers were 28-16, second in the Pacific Division, entering Friday night's game at Toronto.
Gasol, the NBA rookie of the year in 2002 and an All-Star four years later, has averaged 18.8 points and 8.6 rebounds in 476 career games. The 27-year-old is under contract for three more years. The Grizzlies (13-33) haven't won a postseason game since Gasol joined them and haven't made the playoffs since 2006.
The Lakers also signed backup center DJ Mbenga to a second 10-day contract. The 7-footer from the Congo signed his first 10-day contract Jan. 21 and averaged 1.5 points and 1.5 rebounds in four games. Mbenga was released by the Dallas on Oct. 30 and signed with Golden State on Nov. 17, where he played 16 games before being released Jan. 6.