In the video, Woods can been seen walking slowly as an officer puts him through a field sobriety test.
The incident began when Jupiter police noticed his Mercedes pulled awkwardly to the side of the road with the engine running, the brake lights on and a right-turn signal blinking. Both tires on the left side of the car were flat, and police said there was fresh damage to the driver's side.
VIDEO: Excerpts from dashcam footage of Tiger Woods' field sobriety test and DUI arrest
Inside the car, Woods was sound asleep at the wheel, officers reported. Incident reports said his speech was slurred and he didn't know where he was.
At one point during questioning, the officer reported Woods said he thought he had been driving from Los Angeles and was heading to Orange County.
He was unable to tie his shoes and was unable to walk straight on a white line, failing a sobriety test.
A breath test registered 0.0 for alcohol, corroborating what Woods said in a statement issued Monday evening.
"I want the public to know that alcohol was not involved," Woods said. "What happened was an unexpected reaction to prescribed medications. I didn't realize the mix of medications had affected me so strongly."
He was arrested and briefly jailed on suspicion of driving under the influence. He also agreed to a urine test.
It's the first time Woods has run into trouble off the golf course since he plowed his SUV into a tree and a fire hydrant outside his Windermere, Florida, home in the early morning after Thanksgiving 2009, which led to revelations that he had multiple extramarital affairs. He eventually was cited for careless driving and fined $164.
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Woods will be arraigned July 5 in Palm Beach County court on the DUI charge.
The Associated Press contributed to this report.