Buckingham Palace said: "It is with deep sorrow that Her Majesty The Queen announces the death of her beloved husband, His Royal Highness The Prince Philip, Duke of Edinburgh.
"His Royal Highness passed away peacefully this morning at Windsor Castle.
"The Royal Family join with people around the world in mourning his loss."
The Union Flag at Brympton Way in Yeovil has been lowered to half mast, and at other council sites.
In a joint statement, South Somerset District Council's Leader and Chairman said: "We want to send our deepest condolences, those of the people of South Somerset and from all those at South Somerset District Council, to Her Majesty The Queen and her family.
"This is a sad day but one that gives us a chance to reflect on the inspiration that Prince Philip has been to generations of people in the UK and around the world.
"He led a life of dedicated public service by supporting The Queen and in so many other ways.
"He was an extraordinary public servant who will be rightly remembered for both his commitment and devotion to his country."
In view of public safety in the light of current Covid-19 restrictions, a link to the official online book of condolence has been provided.
The Royal Household has suggested that people could make donations to charity instead of flowers, if they wish to do so.
Prince Philip and the Queen had four children, eight grandchildren and 10 great-grandchildren.
Their first son, the Prince of Wales, Prince Charles, was born in 1948, followed by his sister, the Princess Royal, Princess Anne, in 1950, the Duke of York, Prince Andrew, in 1960 and the Earl of Wessex, Prince Edward, in 1964.
Prince Philip was born on the Greek island of Corfu on 10 June 1921.
His father was Prince Andrew of Greece and Denmark, a younger son of King George I of the Hellenes.
His mother, Princess Alice, was a daughter of Lord Louis Mountbatten and a great-granddaughter of Queen Victoria