In a hearing at London's High Court which lasted less than a minute, District Judge Anne Aitken granted Nigella Lawson and Charles Saatchi a decree nisi - the first legal step to ending their 10-year marriage.
Saatchi, 70, and Lawson, 53, now have to wait for a decree absolute, which is usually issued six weeks and a day later, ending their marriage.
Charles Saatchi and Nigella Lawson confirmed they would not make any financial claims against the other, ruling out prolonged legal arguments.
Earlier this year Saatchi accepted a police caution for assault after photographs emerged appearing to show him holding his wife by the throat.
Saatchi later told the Mail on Sunday the pictures gave a "wholly different and incorrect implication".
But he also told the newspaper: "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."
Art collector Charles Saatchi has announced he has filed for divorce from Nigella Lawson - citing her refusal to defend his reputation after he was pictured with his hand around her neck at a restaurant.
In a statement, the 70-year-old told The Mail On Sunday: "I am sorry to announce that Nigella Lawson and I are getting divorced.
"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 couple were pictured on June 9 showing Saatchi with his hand around the 53-year-old celebrity chef's throat.
He was recently cautioned by police after photographs showed him with his hand on the neck and finger up the nose of his wife, the TV chef Nigella Lawson, at a restaurant in London's upmarket Mayfair area.
Mr Saatchi is cited in the Evening Standard as saying that “even domestic goddesses sometimes have a bit of snot in their nose. I was trying to fish it out”.