The snaps were published, against the wishes of St James's Palace, by the same Italian magazine that previously printed topless shots of Kate.
This Morning had intended to only show a blurred version of the magazine cover and apologised unreservedly to the Duke and Duchess.
"Earlier, during today's news review, we were discussing photographs of the Duke and Duchess of Cambridge on a beach in Mustique published in an Italian magazine," Eamonn said.
"Unfortunately, we accidentally showed an unblurred image of the magazine cover, which briefly showed the photographs.
"This was a deeply regrettable error and we are very sorry. We apologise unreservedly to the Duke and the Duchess."
Meanwhile, an Australian magazine has also decided to publish the pictures and rejected issues of privacy as Kate and William were holidaying on a public island.
The editor of Woman's Day, Fiona Connolly, also told Australia's Channel Nine network that the palace's condemnation of the photos being published had backfired because "twice as many people will now want to see them".
A St James's Palace spokesman would not comment on whether William had been informed about the issue, or if they were considering any form of legal action against the magazine.