Prince Philip has died at the age of 99.
An online book of condolence is now available on the royal website for those who wish to send a personal message.
Members of the public have been asked not to leave flowers outside royal palaces, with the Royal Family asking people to consider making a donation to charity instead.
A Death Gun Salute will be fired at midday on Saturday to mark the passing, the MOD said.
A statement from Buckingham 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.
"His Royal Highness passed away peacefully this morning at Windsor Castle."
The Duke of Edinburgh had spent 28 nights in hospital earlier this year, including undergoing heart surgery – his longest ever hospital stay.
The Prime Minister paid tribute to Prince Philip, saying the Duke of Edinburgh had "helped to steer the Royal Family" so that it remained central to national life.
"He was the longest-serving consort in history, one of the last surviving people in this country to have served in the Second World War, at Cape Matapan where he was mentioned in despatches for bravery and in the invasion of Sicily, where he saved his ship by his quick thinking and from that conflict he took an ethic of service that he applied throughout the unprecedented changes of the post-war era," Boris 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."
But above all, he will be remembered for his "steadfast support for Her Majesty the Queen".
"It is to Her Majesty, and her family, that our nation's thoughts must turn today."
Defence Secretary Ben Wallace made his own tribute: "A constant supporter and ambassador of the Armed Forces throughout his lifetime, he will be very much missed by members of the military community.
"As a Royal Navy officer, the Duke of Edinburgh upheld all values that the Armed Forces represent. His leadership, dedication and passion for serving his country is something that all those in uniform can relate to.
"It is only fitting that the Armed Forces will play such a high-profile role in the events to commemorate His Royal Highness' life and lay him to rest.
"The Duke of Edinburgh had a long affiliation with the Royal Navy, having trained at Britannia Royal Naval College in Dartmouth before deploying onboard HMS Ramillies, HMS Kent and HMS Shropshire to serve his country during the Second World War.
"All sailors, soldiers, marines and aircrew are inspired by the example set by their predecessors. The Duke of Edinburgh and his generation will forever be treasured by the Armed Forces for their leadership and sacrifice during the Second World War.
"As we mourn The Duke of Edinburgh and offer our condolences to Her Majesty The Queen, we will remember all that His Royal Highness contributed towards the Armed Forces and be forever grateful for his service."
Labour leader Sir Keir Starmer said the UK had "lost an extraordinary public servant in Prince Philip".
"He will be remembered most of all for his extraordinary commitment and devotion to the Queen," Sir Keir added.
His Royal Highness was the nation's longest-serving consort, having married the Queen on 20 November 1947.
Prince Philip served for more than a decade in the Royal Navy, including in the Second World War when he was mentioned in dispatches.
The Chief of the Defence Staff has also paid tribute.
General Sir Nick Carter said: "It is with great sadness that we heard of the death of His Royal Highness The Duke of Edinburgh this morning. His Royal Highness has been a great friend, inspiration and role model for the Armed Forces and he will be sorely missed.
"The Duke of Edinburgh served among us during the Second World War, and he remained devoted to the Royal Navy and the Armed Forces as a whole. His candour and his humour made many a serviceman and servicewoman chuckle on the countless visits that he made to the Armed Forces.
"He cared deeply about the values, standards and sense of service embodied in the military ethos. He was an immensely popular figure, and he was hugely respected by us all."
US President Joe Biden and First Lady Jill Biden said: "On behalf of all the people of the United States, we send our deepest condolences to Her Majesty Queen Elizabeth II, the entire Royal Family, and all the people of the United Kingdom on the death of His Royal Highness Prince Philip, the Duke of Edinburgh.
"Over the course of his 99-year life, he saw our world change dramatically and repeatedly. From his service during World War Two, to his 73 years alongside the Queen, and his entire life in the public eye — Prince Philip gladly dedicated himself to the people of the UK, the Commonwealth, and to his family.
"The impact of his decades of devoted public service is evident in the worthy causes he lifted up as patron, in the environmental efforts he championed, in the members of the Armed Forces that he supported, in the young people he inspired, and so much more.
"His legacy will live on not only through his family, but in all the charitable endeavours he shaped.
"Jill and I are keeping the Queen and Prince Philip's children, grandchildren, and great-grandchildren in our hearts during this time."
Cover image: Newsphoto/Alamy.