The photos showed Lawson, hugely popular in Britain for her television cooking shows, in tears and brought Saatchi, a former advertising tycoon, a police caution for assault, though he tried to play down the incident as a "playful tiff".
Lawson, 53, the daughter of former British Chancellor Nigel Lawson, said nothing publicly after the row, but groups campaigning against domestic abuse and violence against women complained over the lack of action taken against Saatchi.
A statement from Lawson's publicist confirmed on behalf of the couple that were divorcing, adding that "neither party will be making any financial claims against the other".
Fiona Shackleton, who represented Paul McCartney during his divorce from Heather Mills, was working for Lawson to bring the matter to a "swift and amicable" conclusion, it said.
"Both parties would appreciate privacy for themselves and their children at this difficult time," the statement said.
Lawson, nicknamed the "domestic goddess" after one of her cookery books, married Saatchi in 2003 after her first husband, journalist John Diamond, died of throat cancer. She has two teenage children, Cosi and Bruno, from her first marriage.
Saatchi, 70, ran the world's largest advertising agency Saatchi & Saatchi with his brother in the 1980s.
(Reporting by Belinda Goldsmith, editing by Gareth Jones)