The complicated deal also sends under-achieving center Kwame Brown, guard Aaron McKie, who the Lakers signed earlier in the day for salary cap purposes, the draft rights to Gasol's brother Marc, and first round draft picks in 2008 and 2010 to Memphis.
The key player was the seven-foot Gasol, a former NBA Rookie of the Year.
Gasol, 27, is averaging 18.9 points and 8.8 rebounds in 39 games this season for the Grizzlies (13-33), who are last in the Southwest Division and last made the playoffs in 2006.
"We're extremely pleased to be able to make this trade," said Lakers General Manager Mitch Kupchak. "Pau is a proven player who can score and rebound and we feel this move strengthens our team in the short term as well as the long term."
Memphis also got rookie guard Javaris Crittenton.