He joined former prime ministers Theresa May and Gordon Brown in a deep personal tribute to the late monarch.
A fourth former Prime Minister, Sir Winston Churchill, has been declared by his grandson Sir Nicholas Soames to ‘respect’ the Queen and ‘love her very much’.
Mr Cameron, who led the government from 2010 to 2016, described King Charles as ‘smart and charming’.
He added: “Like his mother, he was a fantastic diplomat. I saw him in action at the Commonwealth Heads of Government Meeting. He knew all the leaders and his interactions with them were exceptional.”
“The soft power that the British monarch brings helps the Prime Minister and the government to manage all these international relations.”
“Under Queen Elizabeth II, it is obviously exceptional. I think you will find that Charles III would be a very worthy successor in this respect.
In a touching anecdote, Mr Cameron continued: ‘When we have to go to a banquet, a dinner or a big meeting, my wife always says, ‘I would like to be seated next to Prince Charles, that’s the best candidate. , it is the most charismatic company”.
“He was also very smart. As we mourn the loss of our greatest monarch, I believe the constitutional monarchy is in good hands. Mr Cameron, Ms May and Mr Brown have all said that under King Charles the monarchy will gradually evolve. “
Mr Brown was joined by fellow former leaders Sir Tony Blair, Sir Boris Johnson, Mr Cameron, Ms May and Sir John Major at a membership committee at St James Palace on Saturday when Charles was officially proclaimed king during the ceremony.
The former Labor leader, who served as prime minister from 2007 to 2010, also told the BBC’s Politics program on Sunday alongside Laura Kunsberg how he believed the new monarch would bring a major change to the approach taken by the Royal family.
He explained: “Charles has shown that the monarchy is going to be smaller. In the future, it will look more like a Scandinavian monarchy, but that’s not a bad thing – more informal. When he entered Buckingham Palace he stopped and spoke to people in the crowd who were talking, it’s a signal from him that he wants people to find him accessible.
Ms May, who served as prime minister from 2016 to 2019, said while she expected the monarchy to continue to adapt to change, people would only appreciate small changes.
“The royal family has constantly developed a different approach, a different way of doing things over time, and I’m sure King Charles will continue to push that forward,” she said.
“He’s a different person and he may want to change things up one way or another, but I think, as the Queen did, it’s important that any change in the way things are done gradually and with great care.”
“I think audiences will expect that sense of continuity and a feeling that the world is always changing, ever-changing, and therefore ready to go with it.”
“What they want and what they get is Her Majesty’s deep concern for people. King Charles has that too – a deep interest in people.
Sir Nicholas has revealed that Sir Winston ‘respected’ the late monarch and shared a warm paternalistic friendship with her.
When she ascended the throne in 1952, he was her first prime minister and she reigned for 70 years, followed by 14 prime ministers.
The grandson of Mr Churchill, Tory MP from 1983 to 2019, said: ‘She loved him and he loved her.
“He has known her since he was a child and he loves her very much.”
Writer and lawyer Caroline Kennedy, daughter of slain former US President John F Kennedy, said the Queen was a “very skilled diplomat and leader”.
His comments were one of thousands of tributes pouring in from around the world.
Australia has announced a public holiday to mark a day of national mourning following the state funeral of the late Queen.
Prime Minister Anthony Albanese has confirmed that he and his Governor General David Hurley will travel to the UK in the coming days for his funeral next Monday.
Mr Albanese also revealed he would not hold a referendum on whether Australia should become a republic in his first term.
He said it was a time to thank the Queen “for her service to Australia, the Commonwealth and the world”.