The Queen's public endorsement of her son is an unprecedented move and came as she officially opened a major Commonwealth summit attended by presidents and prime ministers from across the globe.
Speaking about her wishes is likely to end years of speculation about who will take over as head of the institution her father King George VI first led in the aftermath of the Second World War.
The leaders are due to discuss the issue of Commonwealth succession during the two-day Commonwealth Heads of Government Meeting (Chogm), which will also see leaders debate topics ranging from a blue charter on ocean conservation to cyber security and trade.
With Charles and other senior royals sat in front of her in Buckingham Palace's ballroom, the Queen told the delegates who included Prime Minister Theresa May: "It remains a great pleasure and honour to serve you as Head of the Commonwealth and to observe, with pride and satisfaction, that this is a flourishing network.
"It is my sincere wish that the Commonwealth will continue to offer stability and continuity for future generations, and will decide that one day the Prince of Wales should carry on the important work started by my father in 1949.
"By continuing to treasure and reinvigorate our associations and activities, I believe we will secure a safer, more prosperous and sustainable world for those who follow us: a world where the Commonwealth's generosity of spirit can bring its gentle touch of healing and hope to all."
The prime minister of Malta Dr Joseph Muscat, outgoing chair-in-office of the Commonwealth, also backed Charles as head of the Commonwealth, seeming to confirm the prince's future role was a certainty.
"We are equally elated by the vigour with which His Royal Highness the Prince of Wales actively participates in Commonwealth affairs and puts a strong Commonwealth dimension in his various national and global ventures," Dr Muscat said in a speech at the ceremony.
"We are certain that, when he will be called upon to do so, he will provide solid and passionate leadership for our Commonwealth."
It has been widely assumed that the Queen, who celebrates her 92nd birthday on Saturday, is probably presiding over her last Chogm in person as she has not taken a long-haul flight for a number of years and the venue for the biennial summit moves around the globe, with the UK only hosting it three times in the last 32 years.
The Queen has been head of the Commonwealth since coming to the throne in 1952, but the position is not automatically held by the British monarch.
Downing Street said on Monday that a decision on whether the prince should succeed his mother as Commonwealth head was expected from the presidents and prime ministers on Friday, and reports have stated the mood is Charles will get their backing.
With the UK leaving the European Union the Commonwealth - a collection of former states that were once part of the British Empire - is likely to become increasingly important in terms of trade opportunities for Britain.
Charles has been highlighting his affinity with the Commonwealth in recent years and in his words of welcome to the leaders said: "For my part, the Commonwealth has been a fundamental feature of my life for as long as I can remember, beginning with my first visit to Malta when I was just five years old."
He went on to mention Commonwealth "giants" he had met and talked to like Kenneth Kaunda, the first president of Zambia, and Canada's former prime minister Pierre Trudeau, whose son Justin Trudeau now holds the post and was among the guests.
The prince added: "On the foundations they laid, the modern Commonwealth has a vital role to play in building bridges between our countries, fairer societies within them and a more secure world around them."
Later Dr Keith Mitchell, the prime minister of Grenada, said he had "no difficulty" with Charles taking over as head of the Commonwealth.
He told the BBC: "It would be good news, the Queen herself does very well and certainly we have been fortunate to have her leadership of stable leadership over this period.
"But having the Prince of Wales would certainly not be an unhelpful act at this point in time."
The Prime Minister's official spokesman said: "The Government supports the Prince of Wales as the next head of the Commonwealth."
Ms May's spokesman added. "He has been a proud supporter of the Commonwealth for more than four decades and has spoken passionately about the organisation's unique diversity.
"Succession is a matter for the Commonwealth as a whole to determine. Any discussion that did take place would take place at the leaders' retreat at Windsor Castle on Friday. Decisions in the Commonwealth are made by consensus."
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