The couple separated in June (13) after headline-grabbing photos emerged showing Saatchi with his hand around the British Tv star's throat during an argument outside a London restaurant.
He was cautioned for assault by police, and Lawson subsequently moved out of their family home in London with her two teenage children from her previous marriage to late journalist John Diamond.
Saatchi filed for divorce earlier this month (Jul13), insisting he and his wife had become "estranged" in the past year, and now they have issued a joint statement confirming their intentions to reach a "swift and amicable" split.
The statement reads: "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."
Lawson and Saatchi wed in 2003 and have no children together. He has a daughter from a previous relationship.
Shackleton represented MCCartney in his high-profile divorce from second wife Heather Mills in 2008.