The royal family tweeted a screenshot of the statement, which also said: "I know her loss will be deeply felt throughout the country, the Realms and the Commonwealth, and by countless people around the world."
Queen Elizabeth, Britain's longest-reigning monarch and the nation's figurehead for seven decades, died at her home in Scotland aged 96 on Thursday.
Elizabeth's eldest son Charles, 73, automatically becomes king of the United Kingdom and the head of state of 14 other realms including Australia, Canada and New Zealand. His wife Camilla becomes Queen Consort.