The palace said: “It is with deep sorrow that Her Majesty The Queen has announced the death of her beloved husband, His Royal Highness The Prince Philip, Duke of Edinburgh.
The palace went on to say “His Royal Highness passed away peacefully this morning at Windsor Castle.”
Boris Johnson said he “inspired the lives of countless young people”.
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.
Paying tribute to the duke’s role as the longest serving consort in history, Mr Johnson also remembered Prince Philip as one of the last surviving people to have fought in World War II.
“From that conflict he took an ethic of service that he applied throughout the unprecedented changes of the post-War era,” Mr Johnson said.
“Like the expert carriage driver that he was, 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.”