Isabelle de Rouvre, 74, sold her house, Chalet Helora, to her then-friends Prince Andrew and his ex-wife Sarah Ferguson in 2014 for £18million.
Andrew and Fergie agreed with Ms de Rouvre that the house would be paid for in instalments.
But Ms de Rouvre claimed the Yorks failed to make the final instalment of £5m for the property in the exclusive Swiss ski resort of Verbier.
Initially Ms de Rouvre agreed that it could be deferred until December 2019, with interest accruing, but the pair still did not honour the agreement despite repeated demands.
Glamorous Ms de Rouvre, saddened by the breakdown in trust, was forced to launch a legal battle in the Swiss courts two years ago in an attempt to recoup the sum owed to her by the Duke of York.
The Duke finally paid late last year, and Ms de Rouvre has now said: 'The war is over. He has paid the money.'
The settlement raises questions over how Andrew raised the £6.6million he owed Ms de Rouvre - but it now paves the way for him to sell Chalet Helora and free up desperately needed cash to pay his escalating legal bills due to claims he sexually assaulted Virginia Roberts.
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Disposal of the chalet will leave him owning no property in the UK or abroad.