She was 96 and had received her 15th prime minister, Liz Truss, only two days before.
The King, who said he recalled Her Late Majesty with “great affection”, has released a portrait of her taken by Cecil Beaton in 1968, when she was 42.
In it, she is standing side on to the camera, wearing her Garter robes and the Grand Duchess Vladimir’s Tiara, made of 15 interlaced diamond circles.
In a short statement written and recorded at Balmoral Castle, where the Queen passed away, her son said: “In marking the first anniversary of Her Late Majesty’s death and my accession, we recall with great affection her long life, devoted service and all she meant to so many of us.
“I am deeply grateful, too, for the love and support that has been shown to my wife and myself during this year as we do our utmost to be of service to you all.”
The Prince and Princess of Wales are expected to attend a special service at St Davids Cathedral in St Davids, west Wales, it has been reported, in memory of the Queen.
Rishi Sunak has also paid tribute, noting the late Queen’s “sharp wit”.
With the “perspective of a year”, the prime minister said the “scale of Her Late Majesty’s service only seems greater”.
Remembering his meetings with her, the PM added: “I was struck by her wisdom, by her incredible warmth and grace, but also her sharp wit.”
Turning to Charles, Mr Sunak said that while the country should be proud of the late Queen’s “remarkable legacy of service”, he said a “remarkable bond” between the country and the monarchy “continues to grow today under the reign of His Majesty The King”.
Labour leader Sir Keir Starmer said the late Queen “always enjoyed a special bond with her people”.
He added: “It was a relationship built from her understanding that service of this great nation is the thread that unites sovereign and subject.”
To mark Accession Day, soldiers and horses who took part in the state funeral procession and proclamation salutes signifying the new reign will return to perform anniversary gun salutes in the King’s honour.
Captain Amy Cooper – lead rider in the procession which carried the Queen’s coffin to lie in state in Westminster Hall – will give the order to fire a 41-gun salute at midday in London’s Hyde Park.
A 62-gun salute will also be fired at the Tower of London by The Honourable Artillery Company.
In commemoration of the King’s accession, bells will be rung at Westminster Abbey at 1pm.