Prince Andrew and his ex-wife Sarah Ferguson have bought a luxury chalet, thought to be worth up to £13m, in the Swiss resort of Verbier.
The chalet was bought by the divorced couple on a joint mortgage.
The Duke and Duchess of York have links with the ski resort going back at least 17 years, when they went there on holiday with their two daughters.
The purchase has been described as a "family investment". Buckingham Palace declined to comment.
The chalet was bought on a joint mortgage for a cost of between £8m and £13m.
A source close to the duchess described the purchase as a "family investment".
"They holiday in Verbier several times each year as all the family are keen skiers and it makes sense to have their own place there," the source said.
Although the couple divorced in 1996 after 10 years of marriage, they remained on good terms as they raised their two daughters, Princesses Beatrice and Eugenie, and the duchess lives in the family home of Royal Lodge in Berkshire.
It has been stressed to the BBC that no "external party" provided funding for the purchase.
By royal correspondent Peter Hunt
The timing of this revelation is unfortunate from the perspective of Buckingham Palace.
It focuses attention again on the life that Prince Andrew can afford to lead.
And on the relationship he continues to enjoy with a woman he divorced 19 years ago and who has declared that they are "the happiest divorced couple in the world".
The prince has a modest naval pension and is funded out of his mother's private income.
His ex-wife once had debts of five million pounds.
Together, they've managed to secure a mortgage and buy a Swiss chalet worth millions.
Those around the duchess are keen to stress that the couple haven't borrowed any money from any individuals.
Jeffrey Epstein, the registered sex offender, who once loaned Sarah Ferguson £15,000, hasn't bankrolled this purchase.
The Queen, with her substantial but never disclosed private wealth, may well have underwritten this loan, taken out by the parents of two of her grandchildren.
News of the property purchase comes a week after the Duke of York, the Queen's second son, was named in US court papers relating to a case against American financier Jeffrey Epstein.
Royal officials have said Prince Andrew will "move on and push ahead" with his work amid the claims made in the case that Mr Epstein pressured a young woman to have sex with the duke on three occasions between 1999 and 2002.
Buckingham Palace has "emphatically denied" the allegations.