A statement issued by the palace just after midday spoke of the Queen’s “deep sorrow” following his death at Windsor Castle on Friday morning.
The Duke of Edinburgh, the longest-serving royal consort in British history, was at the Queen’s side for more than her six decades of reign.
Boris Johnson said he “inspired the lives of countless young people”.
“It is with deep sorrow that Her Majesty The Queen announces the death of her beloved husband,” the Palace said.
“The Royal Family join with people around the world in mourning his loss.”
It is understood that the Prince of Wales travelled from his home in Gloucestershire to visit his mother at Windsor Castle on Friday afternoon.
Speaking at Downing Street, the prime minister said that the duke had “earned the affection of generations here in the United Kingdom, across the Commonwealth, and around the world”.
Meanwhile, Justin Welby, the Archbishop of Canterbury, said he “consistently put the interests of others ahead of his own and, in so doing, provided an outstanding example of Christian service”.
In tribute to the duke, Westminster Abbey began tolling its tenor bell once every 60 seconds at 18:00 BST. It rang out 99 times to honour each year of his life.
Earlier, the flag at Buckingham Palace was lowered to half-mast and a notice was posted on the gates to mark the duke’s death.
People placed floral tributes outside the palace, while hundreds visited Windsor Castle to pay their respects.
However, the government urged the public not to gather or leave tributes at royal residences amid the coronavirus pandemic.
The Royal Family has asked people to consider making a donation to a charity instead of leaving flowers in memory of the duke, and an online book of condolence has been launched on the official royal website for those who wish to send messages.
A message on the website of the Duke and Duchess of Sussex’s non-profit organisation Archewell paid tribute to the “loving memory” of the Duke of Edinburgh, saying: “Thank you for your service… you will be greatly missed.”
From midday on Saturday, a 41-gun salute will take place for Prince Philip in cities including London, Edinburgh, Cardiff and Belfast, as well as in Gibraltar and at sea from Royal Navy warships, the Ministry of Defence said. They will be broadcast online and on television for the public to watch from home.
The BBC’s royal correspondent Nicholas Witchell said it was “a moment of sadness” for the country and “most particularly, for the Queen losing her husband of 73 years – a bigger span of years than most of us can imagine”.
He said Prince Philip had made “a huge contribution to the success of the Queen’s reign”, describing the duke as “utterly loyal in his belief in the importance of the role that the Queen was fulfilling – and in his duty to support her”.
“It was the importance of the solidity of that relationship, of their marriage, that was so crucial to the success of her reign,” he added.
A bank of photographers and cameramen were lined up around the growing number of tributes at Buckingham Palace on Friday afternoon, said BBC News reporter Marie Jackson.
Rhea Varma, from Pimlico, pulled up to the gates on her bike to lay flowers and a note saying Rest in Peace Duke.
She said the news was “super sad”. To her, the duke was “the kind of stability that’s so old-fashioned it’s difficult to comprehend. He was a rock who brought integrity.”
Adam Wharton-Ward, 36, also arrived to leave lilies by the palace gates. He is visiting London from his home in France but was so moved by the news, he wanted to “rally round” for the Queen’s sake.
“It’s so sad. He’s been with her for 73 years. If it wasn’t for him who knows if she would have got through it,” he said.
The duke’s appeal, he added, was that he was “almost normal with his gaffes”.
“Now that normality has gone,” he said.
The prince married Princess Elizabeth in 1947, five years before she became Queen.
In March, the duke left King Edward VII’s hospital in central London after a month-long stay for treatment .
He was admitted on 16 February after feeling unwell, and later underwent a procedure for a pre-existing heart condition at another London hospital – St Bartholomew’s.
This is a town that’s seen many royal events over the years, both happy and sad.
Today, it is one of quiet reflection.
The sun has been shining down on Windsor Castle this afternoon, but the mood outside is understandably sombre.
As locals heard of the duke’s death they turned up to leave flowers outside the entrance.
One young boy, Oscar, came with his mother to lay flowers. He left a card which read: “Your Majesty, so sorry about hearing about your amazing husband.”
“It’s really sad,” another woman told us. “I just wanted him to get to 100,” she said.
The flag here hasn’t been lowered to half-mast. That’s because it’s the Royal Standard which means the Queen is in residence. It’s the one flag which remains at full mast.
It was here that the duke spent his last weeks after being discharged from hospital.
Inside the castle the Queen, now a widow, is in mourning for her husband who has always been by her side.
Prince Philip’s funeral will take place at St George’s Chapel, Windsor – but the arrangements have been amended in light of the coronavirus pandemic, the College of Arms said in a statement .
It added that the funeral will not be a state funeral, and the duke will not lie in state.
The duke will, however, lie at rest in Windsor Castle ahead of a funeral, the College of Arms said, “in line with custom and with His Royal Highness’s wishes”.
The statement said: “The funeral arrangements have been revised in view of the prevailing circumstances arising from the Covid-19 pandemic and it is regretfully requested that members of the public do not attempt to attend or participate in any of the events that make up the funeral.”
Buckingham Palace will confirm the detailed arrangements for the funeral on the Royal website, it added.
All UK government buildings have been told to fly an official flags at half-mast in tribute to the duke until 08:00 BST on the day after the funeral.
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 Prince Louis of Battenberg and a great-granddaughter of Queen Victoria.
Politicians across the UK were united in mourning following the announcement of the duke’s death.
Labour leader Sir Keir Starmer said the UK had “lost an extraordinary public servant”, while Scotland’s First Minister Nicola Sturgeon said his “long contribution to public life in Scotland will leave a profound mark on its people”.
Wales’ First Minister Mark Drakeford said the duke “served the crown with selfless devotion and generosity of spirit”.
Parliament will honour the duke on Monday, with the House of Commons sitting at 14:30 BST for tributes following his death.
Parties have also suspended their campaigning elections on 6 May, which will see voters head to the polls for council and mayoral positions in England, the Scottish Parliament and Welsh Parliament.
Meanwhile, Commonwealth leaders led international reaction to the duke’s death.
Australian Prime Minister Scott Morrison tweeted that the duke “embodied a generation that we will never see again”, while Canada’s Prime Minister Justin Trudeau described Philip as a “man of great purpose and conviction”.
And Indian Prime Minister Narendra Modi recalled the duke for his “distinguished career in the military” and work “at the forefront of many community service initiatives”.
US President Joe Biden and First Lady Jill Biden joined other world leaders in sending their “deepest condolences” to the Queen, the Royal Family and the people of the UK.
In a statement, they said the duke “gladly dedicated himself to the people of the UK, the Commonwealth, and to his family”.
“His legacy will live on, not only through his family, but in all the charitable endeavours he shipped,” it said.
The palace said further announcements would be made “in due course”.