In a statement shortly after midday, the palace said: “His Royal Highness passed away peacefully this morning at Windsor Castle.”
The duke, who was the longest-serving consort in British history, had returned to Windsor Castle on 16 March after spending a month in hospital.
The UK prime minister, Boris Johnson said he “inspired the lives of countless young people”.
The palace said further announcements would be made “in due course”.
“The Royal Family join with people around the world in mourning his loss,” the statement added.
Speaking at Downing Street, the prime minister added: “He helped to steer the Royal Family and the monarchy so that it remains an institution indisputably vital to the balance and happiness of our national life.”
Mr Johnson said he received the news of the duke’s death “with great sadness”.
“Prince Philip earned the affection of generations here in the United Kingdom, across the Commonwealth, and around the world,” he said.
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