Tabloid newspapers last month published photos of the incident, which Saatchi described as a "playful tiff" during an intense debate about the couple's children.
The 70-year-old Saatchi was given a police "caution" after admitting assault.
He told Britain's Mail on Sunday newspaper that he was "sorry" to announce he will be divorcing Lawson, adding that they have become "estranged" and drifted apart over the past year.
"'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 said.
In what the tabloid called an "exclusive statement" breaking the news to Lawson, Saatchi also suggested that Lawson had herself grasped his neck in a similar fashion in the past.
The Mail on Sunday said that Lawson was not made aware of the divorce move prior to publication.
Lawson and Saatchi married in 2003 and lived in London with Lawson's son and daughter from her marriage to journalist John Diamond, who died of cancer in 2001, and Saatchi's daughter from a previous marriage.
Lawson's spokesman Mark Hutchinson who previously has confirmed that she and her children left the family home after the photos were published declined to comment on Saatchi's statement.
Lawson is a well-known TV presenter and chef whose cookbooks are best-sellers in Britain and the United States.
Saatchi, co-founder of the Saatchi & Saatchi ad agency, owns one of London's biggest private art galleries. He was the main patron of the Young British Artists movement of the 1990s, which made household names of artists including Damien Hirst and Tracey Emin.