The pictures have rekindled memories in Britain of the media pursuit of William's mother, Princess Diana, who was killed in a car crash in Paris in 1997 while being chased by paparazzi.
Britain's tabloid papers, fighting for their reputations after a series of scandals, have refrained from publishing the pictures, even though they are available on the Internet and in the pages of a tabloid in neighboring Ireland.
Lawyers for the royal couple will make the request at a Paris court on Monday, also seeking damages from the French magazine, Closer, and an injunction against the publication of further images.
"We can confirm that a criminal complaint is to be made to the French Prosecution Department tomorrow," said a spokeswoman for the second in line to the British throne and his wife of 16 months, Britain's future queen.
"The complaint concerns the taking of photographs of the Duke and Duchess of Cambridge whilst on holiday and the publication of those photographs in breach of their privacy."
Closer has defended its publication of a dozen long-lens shots of the duchess, the former Kate Middleton, on holiday at a secluded villa in southern France. They show her slipping off her bikini top, relaxing topless on a sun lounger and pulling down her bikini bottoms as her husband applies lotion.
William's office has branded the photos as a "grotesque and totally unjustified" invasion of their privacy.
Even the best-selling Sun tabloid, the only British title to run pictures of William's brother Harry cavorting naked in a Las Vegas hotel last month, has declared the photos off-limits.
As well as fearing new regulation, the British press are wary of upsetting readers just as the royal family's popularity is rising, boosted by William and Kate's glittering wedding last year, this year's Golden Jubilee celebration for Queen Elizabeth, and royal appearances at the London Olympics.
The Irish Daily Star did publish shots of the duchess on Saturday that were originally printed in Closer.
But on Sunday its co-owner, Independent News and Media (INM), Ireland's biggest media company, joined its British partner Northern and Shell in condemning what it called a "breach of decency".
"On behalf of INM, I wish to offer my deepest apologies," INM chief executive Joe Webb said in the Sunday Independent, another of the group's titles.
Northern and Shell Chairman Richard Desmond said he was taking immediate steps to close down their joint venture, but Webb said he hoped to prevent the closure of the paper.
In Italy, where Closer's sister publication Chi was due to publish a special edition on Monday including 26 pages of the photos, Silvio Berlusconi's daughter Marina denied that the former premier had turned down a request by Buckingham Palace not to publish.
Both Chi and Closer are published by Italy's Mondadori, part of Berlusconi's media empire and chaired by his daughter.
"My father is a politician and, with all respect, is busy with other things and has no time to think about a photo reportage," Marina Berlusconi wrote in a vitriolic letter to the daily La Repubblica, which reported the allegation.
"Secondly, Mondadori, which I chair, is a publisher that uses to the best of its ability the freedom that its shareholders have always given it," she wrote.