Saatchi, 70, was accused in June of allegedly choking Lawson, 53, while they were dining at a restaurant. A representative for Lawson confirmed she moved out of the couple's $20.9 million home with their children after the row.
In his announcement, Saatchi criticized Lawson for not defending him after the alleged incident, London's The Sun reported.
"This is heart-breaking for both of us as our love was very deep, but in the last year we have become estranged and drifted apart," 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."
The Sun reported Lawson was unaware of Saatchi's intent to divorce her until she saw reports in Sunday's newspaper.
The couple have been married since 2003 and share a daughter, Cosima, 19, and son Bruno, 17.