Media are reporting today that Saatchi accepted a caution for assault after he was questioned by police officers for five hours.
The 70-year-old multimillionaire art collector had earlier tried to dismiss pictures of him with his hands round his wife's throat as a "playful tiff".
Britain's Sunday People newspaper published photographs of Saatchi with his hands around his wife's neck, and with her in tears, while they were having dinner on the terrace of a London restaurant.
Saatchi was also photographed pinching 53-year-old Lawson's nose before walking away from a seafood restaurant in upmarket Mayfair on June 9.
Police today said: "Officers from the Community Safety Unit at Westminster were aware of the Sunday People article which was published on 16 June and carried out an investigation.
"This afternoon a 70-year-old man voluntarily attended a Central London police station and accepted a caution for assault."
Saatchi, who writes a column for The Evening Standard, had told the newspaper that he recognised the impact of the pictures but said they conveyed the wrong impression.
"About a week ago, we were sitting outside a restaurant having an intense debate about the children, and I held Nigella's neck repeatedly while attempting to emphasise my point," he said.
"There was no grip. It was a playful tiff. The pictures are horrific but give a far more drastic and violent impression of what took place. Nigella's tears were because we both hate arguing, not because she had been hurt."
He said the couple made up by the time they reached home. But he acknowledged that Lawson had moved out, saying this was for her privacy.
