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."
More top news
The mother of "bucket list" cancer patient Stephen Sutton has said signs of her son's illness were "ignored".
Boxing champion and occasional actor Mike Tyson has been praised for coming to the aid of a motorcyclist injured in a crash in Las Vegas.
A website is threatening the release of hacked nude pictures of Emma Watson, reportedly in response to her speech on gender equality.