The art tycoon earlier denied that the pictures were evidence of anything more than a "playful tiff".
He was interviewed at Charing Cross police station on Monday evening, when he was cautioned by police over the incident outside Scott's restaurant in Mayfair.
"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," a spokesman for the Metropolitan Police confirmed. "This afternoon a 70-year-old man voluntarily attended a central police station and accepted a caution for assault."
Celebrity chef Nigella is yet to comment on the photos.
In Monday's Evening Standard, her husband said, "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.
"There was no grip, it was a playful tiff. Nigella's tears were because we were both arguing, not because she had been hurt.
"We had made up by the time we were home. The paparazzi were congregated outside our home after the story broke yesterday morning, so I told Nigella to take the kids off till the dust settled."
Charles and Nigella, 53, have been married since 2003. She has two children, Cosmina and Bruno, from her marriage to John Diamond, who died in 2001.
Nigella's spokesman has confirmed that she left the family home with her children, but did not say whether it was a permanent or temporary move.