The couple, both worth millions, said the divorce will be “undefended” and a decree nisi will be pronounced before the end of this month.
The pair separated in the aftermath of a photograph being published in which Saatchi was seen holding his wife by her throat, and he agreed to accept a police caution for assault as a result.
They also confirmed that Fiona Shackleton, who represented Paul McCartney during his divorce from Heather Mills, was working on behalf of Lawson to bring the matter to a “swift and amicable” conclusion.
A statement issued on behalf of Lawson and Saatchi said: “We can confirm that Fiona Shackleton is acting for Nigella Lawson to ensure a swift and amicable resolution. A divorce will proceed on the undefended basis, the decree nisi is to be pronounced on 31 July, and neither party will be making any financial claims against the other.
“Contrary to some reports, Charles Saatchi has not consulted lawyers and has represented himself throughout.
“Both parties would appreciate privacy for themselves and their children at this difficult time.”
Photographs of TV chef Lawson, 53, and Saatchi, 70, were published a month ago that showed him holding her by the throat on the terrace of a restaurant.