Saatchi, 70, a wealthy art collector and global ad agency co-founder, was pictured clutching Lawson by her throat at a London restaurant on June 9, reported People magazine.
"I am sorry to announce that Nigella Lawson and I are getting divorced," Saatchi said in a statement.
"I feel that I have clearly been a disappointment to Nigella during the last year or so, and I am disappointed that she was advised to make no public comment to explain that I abhor violence of any kind against women, and have never abused her physically in any way," he added.
But in his statement, Saatchi downplayed the fight with Lawson, 53, with whom he has been married for 10 years.
"This is heartbreaking for both of us as our love was very deep, but in the last year we have become estranged and drifted apart. The row photographed at Scott's restaurant could equally have been Nigella grasping my neck to hold my attention - as indeed she has done in the past," the statement said.