Charles became king immediately following the death of his mother Queen Elizabeth II, but a historic meeting formally confirmed his role on Saturday.
During the Accession Council, the King approved the day of the Queen's funeral becoming a bank holiday, although it is not known when it will take place.
It is the first time the historic ceremony has been televised.
The King himself was not present to begin with, but he attended the second part of the ceremony to hold his first meeting of the Privy Council, the group of senior politicians who advise the monarch.
Clerk of the Privy Council Richard Tilbrook proclaimed Charles "King, head of the Commonwealth, defender of the faith", before declaring "God Save the King".
The packed room, attended by senior politicians, judges and officials who gathered in the State Apartments of the Palace in London, repeated back the phrase.
Making his own declaration, the King said it was his "most sorrowful duty" to announce to the death of his mother.
He said: "I know how deeply you, the entire nation, and I think I may say the whole world, sympathise with me in the irreparable loss we've all suffered.
"It is the greatest consolation to me to know the sympathy expressed by so many to my sister and brothers."
The ceremony was attended by 200 members of the Privy Council, including former Prime Ministers Boris Johnson, Theresa May, David Cameron, Gordon Brown, Tony Blair and John Major.
Later, applause and cheers of "God Save the King" broke outside St James's Palace, before a crowd of thousands sang the national anthem.
It was the decision of King Charles III to allow television cameras into the Accession Council for the first time to allow the public to view proceedings.
