Odom, 33, was released after posting $15,000 bond and is expected in Van Nuys Municipal Court on Sept. 27.
The 6-foot-10 forward, who most recently played with the Clippers and is now a free agent, was arrested Friday morning after a California Highway Patrol officer observed him driving erratically on the 101 Freeway in the San Fernando Valley, officials said.
A CHP report notes that Odom was driving in a "serpentine manner." He showed signs of being under the influence of either drugs or alcohol and failed a field sobriety test, according to the CHP.
At the Van Nuys jail, Odom refused all chemical tests and was booked without incident, CHP officials said.
He was booked into custody at 5:01 a.m. and released at 8:33 a.m.
Odom's agent, Jeff Schwartz, could not immediately be reached for comment.
Odom has made headlines in recent weeks for alleged drug use, including reports last weekend that he was missing after a fight with his wife, Khloe Kardashian Odom.
His agent told ESPN that the basketball player was "not missing," and a source told the outlet that Odom was at a Los Angeles hotel as friends tried to help him with a drug problem.
Kardashian Odom tweeted about the reports, saying it was "really hard to sit here and listen to people talk … about my family."