The couple were not at London's High Court today for the settlement of their libel action against Times Newspapers Ltd.
The 54-year-old monarch's solicitor, Mark Thomson, said the July 2011 article - which appeared two days after their wedding - accused the prince of having the princess's passport confiscated at Nice airport to prevent her from fleeing Monaco.
It suggested she was reluctant to marry because she had discovered the existence of a third love child, but agreed to the marriage for the sake of appearances in return for payment with a view to obtaining an annulment after a seemly interval.
"None of these allegations are true," Mr Thomson told Mr Justice Eady.
He said that the newspaper had admitted that they were untrue and accepted liability for making such defamatory claims.
It had apologised and confirmed it would pay the couple damages, to be assessed at a later stage if not agreed, and their legal costs.