The couple, jointly worth around £150million, have also agreed to make no financial claim against each other.
Nigella, 53, who is planning to move to the States, has been flooded with offers from US networks to give her side of the story in an exclusive TV interview.
But the domestic goddess and her advertising executive husband have both agreed to keep mum about the reasons behind the split.
The TV favourite has also agreed to make no claims on 70-year-old Charles’s modern art collection.
The couple confirmed yesterday that Fiona Shackleton, Nigella’s cousin who represented Sir Paul McCartney, 71, during his divorce from Heather Mills, 45, was the only lawyer working on bringing it to a “swift and amicable” conclusion.
In a joint statement they said: “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.”
Legal experts said that the speed with which the divorce was going through was a sign that the couple had agreed a confidentiality clause and also had a pre-nuptial deal in place from 2003 when they wed.
Mum-of-two Nigella split from her husband after Saatchi was photographed grabbing her throat during a meal in a top London restaurant.
Saatchi later accepted a police caution for assault.