The decision was made by the 53 leaders on a retreat at Windsor Castle, but will not be confirmed until a press conference later today.
The backing for the Prince of Wales appeared inevitable from the moment that the 91-year-old Queen made a personal request for her son to succeed her, on Thursday.
However, some have opposed it, arguing the role is not hereditary and it would be better to rotate it between countries in the Commonwealth.
On Thursday, Prince Charles himself made an informal pitch to take over the leadership, making clear his commitment to the organisation. “For my part, the Commonwealth has been a fundamental feature of my life for as long as I can remember,” he told the Commonwealth Heads of Government Meeting.