The first hearing will be held today in the family division of the High Court in London and the divorce will be finalised before the end of May.
The Queen, who has been informed of the couple's decision, was said to be "saddened". But royal-watchers said she was relieved by the announcement which comes just before her 70th birthday on Sunday.
The solicitors for the Prince and the Duchess declined to discuss the terms of the divorce, though they said the Duchess would relinquish the title " Her Royal Highness" and will look after their children. Buckingham Palace stressed that the Duke and Duchess, married in 1986 and separated in 1992, remain "close friends" and were under no pressure from the Royal Family to divorce.
A Palace spokesman denied the Queen had written to the Duke and Duchess in the same manner as she wrote to the Prince and Princess of Wales, calling for an end to the marriage.
Financial arrangements between the Duke and Duchess were "entirely a personal matter" and were not being discussed with the media.
Solicitors for the Prince and the Duchess also declined to discuss the terms of the divorce. They issued a joint statement saying: "The Duke and Duchess of York today announced ... that they have agreed, after more than two years' separation, that their marriage should formally be ended. Accordingly the necessary legal proceedings are under way and it is anticipated that the Decree Absolute will be made at the end of May.
"The decision by the Duke and Duchess is a personal one, and theirs alone. Her Royal Highness The Duchess of York has chosen not to use the style `Her Royal Highness' and will continue to be the Duchess of York ... The children will continue to live with the Duchess..."
The royal divorce is listed for hearing today in the Principal Registry of the High Court Family Division at Somerset House, London.
The case, listed as "HRH The Duke of York v HRH The Duchess of York", is the last in a list of 29 "quickie" special procedure divorces to be disposed of under the fast track system before Senior District Judge Gerald Angel. Barring any objections, decrees nisi will be granted in all 29 petitions "en bloc" after the names of each couple have been read out.
It is understood that the Duchess will continue to live at her rented home, Kingsbourne, at Wentworth.
The 36-year-old Duchess is in the middle of a skiing holiday in Switzerland with her children. A spokeswoman for her said: "There is no further comment."
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