The decision will be taken collectively by Commonwealth heads of government, who are holding a private retreat at the royal residence west of London. Prince Charles was confirmed as the next head of the Commonwealth on Friday.
The role is not hereditary, but the Queen, who turns 92 on Saturday, used the ongoing Commonwealth heads of government (Chogm) gathering in London to say it was her "sincere wish" to be succeeded by her son.
The prime minister attended different sessions of the meeting on Thursday and Friday.
The announcement had been expected since the queen said Thursday that she hoped her son and heir would lead the Commonwealth after her.
Paying tribute to Queen Elizabeth II, the President recounted the two visits paid to Ghana, in 1961 under the leadership of Ghana's first President, Dr. Kwame Nkrumah, and in 1998 under President Jerry John Rawlings, by the British Monarch.
If you're not hip to British parlance, the Commonwealth of Nations - formerly known as the British Commonwealth - is an intergovernmental organization of 53 member states, most of which are former territories of the British Empire, such as Canada, India, and Australia.
Expressing her preference for the first time, the Queen said it was her honest wish it would one day decide to have Prince Charles, her oldest child, "carry on the important work started by my father in 1949".More news: Ariana Grande pays tribute to Manchester victims in new single
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Gay-rights activists are also protesting the summit, urging the repeal of laws against homosexuality that are in effect in more than 30 Commonwealth countries - in many cases, introduced under British rule. On Friday the 69-year-old heir to the British throne got another position to wait for - he was approved as the next head of the Commonwealth made up of the United Kingdom and the countries that once were its colonies. "Both as a symbol of our free association, and through deep personal identification with the highest ideals of respect and understanding, Her Majesty has won a place of great affection in the hearts of people in all countries of the Commonwealth", she said.
Joseph Muscat, Prime Minister of Malta and outgoing chair of the Commonwealth is believed to have been instrumental in garnering support for Prince Charles. Some have suggested that Charles should not take over the helm of the group, which takes in 2.4 billion people on five continents.
"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 initiatives".
Others are skeptical that increased Commonwealth trade can make up for reduced access to Britain's biggest market, the EU.
"At Windsor we discussed our vision for the Commonwealth in We have pledged to work together to foster a fairer, more secure, more sustainable and more prosperous future to the benefit of all Commonwealth citizens".
The Commonwealth of Nations has been an institution since 1931, but it is not without its critics.