The footage has been released by Jupiter Police Department, and shows the 14-time major victor struggling to walk during his failed sobriety test.
Woods told police he had taken several prescriptions.
"I understand the severity of what I did and take full responsibility for my actions", the 41-year-old father of two said in the statement.
"I'm following the light", Woods says, his words running together.More news: Nunes-led House Intelligence Committee asked for 'unmaskings' of Americans
Tests corroborated Woods' claim that he did not have alcohol in his system and during the video he is seen to explain that the only drugs he has taken are those he is prescribed. Woods, who has been rehabbing from back surgery, said he did not realize the mix of medications "had affected me so strongly".
Woods announced last week that he had undergone another back surgery in April, his fourth since March 2014. He also agreed to a urine test. Woods apologised to his fans and pledged to "do everything in my power to ensure this never happens again". Laci Kay Somers told TMZ Wednesday that multiple reports of her being with Woods in Florida Sunday night are made up.
On the video, the officer is heard telling Woods to tie his left shoe.
"I am following the light", Woods replied, jabbing his finger awkwardly at it.
Woods will appear in Palm Beach County Court on 5 July charged with drinking under the influence.More news: Andy Murray overcomes tough Del Potro in French Open
The police photos of Woods' 2015 black S63 AMG Mercedes (which sold for a base retail price of about $235,000) show minor damage to the front bumper on the driver's side, as well as scuffs and scratches on the rear bumper.
Woods has won 14 major tournaments, second only to Jack Nicklaus. The latest operation has ruled him out for the rest of the PGA Tour season.
"You can overcome a DUI if you are a big enough star and you keep winning", said Bob Dorfman, creative director of Baker Street Advertising in San Francisco.
During the roadside stop, police administered a series of sobriety tests.More news: Tories chase majority of 80 by campaigning in Labour seats
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