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Sources said he had found a buyer for the chalet and the sale was proceeding.
Isabelle de Rouvre, 74, had waged a two-year legal battle to recoup the money owed to her by the Duke of York.
Now she said: “The war is over. He has paid the money.”
A source close to the Duke told The Standard: "I can confirm that the legal action has been halted and that the chalet is being sold - but otherwise no comment on private financial matters."
Ms Rouvre sold Chalet Helora to Prince Andrew and Fergie for £18million in 2014.
She launched legal action when she claimed the former royal couple failed to make the final instalment of £5m for the property.
However, she has now revealed the payment has been made.
Ms de Rouvre added to The Daily Mail: “I sold it two months ago, or was it one. Maybe six weeks ago. Anyway, I sold it to the Yorks and we made an agreement. That is the end of the story thankfully.”
The Duke of York is believed to be selling the chalet, in the Swiss ski resort of Verbier, to pay his team of US lawyers who he has hired for his legal battle with Virginia Giuffre.
Prince Andrew faces a sex abuse case in a US court.
Ms Giuffre is seeking unspecified damages as she sues the Queen’s son for allegedly sexually assaulting her when she was 17 in a civil case brought against the royal in the US. He denies the allegations.
Watch: Prince Andrew in ‘difficult situation’, says royal correspondent