In a statement recorded at Balmoral Castle, the King also thanks people for the “love and support” shown to him and the Queen in the last year.
The King has remembered his late mother’s “devoted service” and “all she meant” to the country on the first anniversary of her death.
Queen Elizabeth II died on 8 September last year.
She was 96 and had received her 15th prime minister, Liz Truss, only two days before.
The King, who said he recalled his mother 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 Queen Elizabeth died, 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 Queen Elizabeth.