The Braveheart star, 50, was arrested in Malibu, California, on Friday morning when cops spotted him speeding at 80 mph on a 50 mph road. The actor failed both breath and field sobriety tests.
In a statement, Gibson says, "I acted like a person completely out of control when I was arrested and said things that I do not believe to be true and which are despicable.
"The arresting officer was just doing his job and I feel fortunate that I was apprehended before I caused injury to any other person.
"I disgraced myself and my family with my behavior and for that I am truly sorry.
"I have battled with the disease of alcoholism for all of my adult life and profoundly regret my horrific relapse."
While Gibson does not elaborate on the "despicable" comments he made, entertainment website TMZ.com have obtained a police incident report, which alleges the Hollywood star made anti-Semitic comments towards arresting officers.
Gibson was released on $5,000 bail after he was charged with drunk driving.
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