The Rupert Murdoch-owned tabloid made the public statement, after being criticised for publishing images of Prince Harry naked on holiday in Las Vegas.
Posting on the Sun Newspaper Twitter feed, the publication said: "The Sun's editor Dominic Mohan confirmed today that the paper will not publish the topless photographs of Kate Middleton."
Earlier today, a royal spokesperson said that the Duke and Duchess of Cambridge were hugely saddened by the decision of French publication Closer to print the pictures, taken of the Duchess while the couple were on a private holiday in France.
The royal couple view this as a "grotesque and unjustifiable invasion of privacy" by the magazine, the spokesman added.
They are now said to be considering legal action against the publication.
However, Closer's editor Laurence Pieau said that the images were "not in the least shocking" and described the reaction as "disproportionate".
"They show a young woman sunbathing topless, like the millions of women you see on beaches," she said.
Lord Embley, the editor of The Mirror and Sunday Mirror, said that his papers were offered pictures of the Duchess in a bikini a week ago but turned them down.
The titles also did not follow The Sun in publishing the Harry pictures, after judging in both cases that there was a clear breach of the editors' code of practice involving a breach of privacy.
In a lengthier statement discussing the Kate Middleton pictures, The Sun's Mohan said: "The circumstances are very different to those relating to the photos of Prince Harry in Las Vegas.
"As we said at the time, he was at a party in a hotel suite with a large group of strangers and one of those present released a photograph into the public domain."
A year of the Duchess of Cambridge:
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