The 33-year-old was pulled over around 3:25 a.m. for driving too slowly on the eastbound 101 Freeway near Sepulveda. Authorities say Odom was driving in a "serpentine manner" at 50 mph.
When California Highway Patrol tried to pull him over, officials say Odom drove about three more exits before getting off at Coldwater Canyon and stopping his vehicle just south of the freeway.
Authorities say Odom showed obvious signs of intoxication and was unable to perform a field sobriety test.
He was arrested and transported to LAPD's Van Nuys Jail and booked without incident. Authorities said Odom refused to take a blood test. Following state law, his driver's license was immediately suspended.
"He lost his license for a year. He does have a copy of that form, so he knows the reason why he lost his license. He was given opportunity to correct. So if he wanted to, he could change his mind at any point in time during the booking process as well, but he did not do that," said Leland Tang with the CHP.
Odom was held on $15,000 bail. As of 11 a.m., officials said he posted bail, but Odom was not seen physically leaving the building.
The arrest comes at a tumultuous time in Odom's life. Earlier this week, there were reports that his wife, reality star Khloe Kardashian Odom, was trying to help him get clean from alleged drug abuse. There are reports that he is fighting an addiction to crack cocaine.
The 6-foot-10-inch forward has played for the Los Angeles Lakers and Clippers, the Miami Heat and Dallas Mavericks.
Odom broke into the NBA with the Clippers in 1999, playing for them for four seasons before spending the 2003-04 season with the Heat.
He had his best years during his six seasons with the Lakers, beginning in 2004-05. The team won NBA championships in 2010 and 2011 and Odom won the NBA's sixth man award in 2011.
After spending the 2012 season with the Dallas Mavericks, he returned to the Clippers last year. He became a free agent at the end of the season.
The Associated Press contributed to this report.