The paperwork also reveals that an "order for financial relief" between the couple has been approved, suggesting they have come to a private financial agreement without recourse to the courts.
Speculation over the state of their marriage erupted after a British Sunday newspaper published photographs last month which showed Saatchi holding his wife by the throat as they had an argument on the terrace of a restaurant.
He dismissed the incident as nothing more than "a playful tiff", but then accepted a police caution for assault. He said he had done so to stop the incident "hanging over" them.
Lawson, who was subsequently pictured without her wedding ring, has described him as "the exploder" in the past because of his temper.
Saatchi later told the Mail on Sunday that 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."
The couple confirmed they would not make any financial claims against each other, ruling out prolonged legal arguments.
Lawson has been represented by her cousin, Baroness Shackleton, the leading divorce solicitor who represented Sir Paul McCartney when he separated from Heather Mills. Saatchi has not been using any lawyers.