Odom is the first Lakers player ever to win the award, which began in 1983. He averaged 14 points and 9 boards per game coming off the bench this season.
Odom's teammates and reality TV star wife Khloe Kardashian were at the award news conference to celebrate with him.
Odom received 96 of 117 first-place votes from the media panel, easily outdistancing Dallas guard Jason Terry, who finished a distant second with 244 total points to Odom's 513.
Philadelphia's Thaddeus Young was third with 76 points, and Boston's Glen Davis finished fourth with 75.
Atlanta's Jamal Crawford won the award last season.
The Associated Press contributed to this report.
