The portrait of the late Queen has not been released before
In the message, the King said he recalled the late Queen's "devoted service and all she meant to so many of us".
The photograph chosen by the King shows a young Queen, then 42, at an official portrait sitting in 1968.
Elizabeth II died aged 96 at Balmoral Castle on 8 September last year.
It came just months after her Platinum Jubilee marking her 70 years on the throne.
In his short tribute, which will be released on Friday, the King thanked the nation for the "love and support" shown to him and Queen Camilla during his first year as monarch.
"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," the King said.
"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."
His written message, which accompanies the audio recording, is signed Charles R.
The late Queen died at Balmoral Castle on 8 September last year
The formal colour photograph was taken by Cecil Beaton on 16 October 1968 and has not been released until now.
It shows the late Queen standing sideways and smiling in her Garter robes, wearing the Grand Duchess Vladimir's Tiara, made of 15 interlaced diamond circles.
In his own message, Prime Minister Rishi Sunak said the scale of the late Queen's service "only seems greater" a year after her death.
"Her devotion to the nations of the United Kingdom and the Commonwealth only seems deeper," he said.
"And our gratitude for such an extraordinary life of duty and dedication only continues to grow."
Mr Sunak said he treasured his memories of meeting the late Queen in which he was struck by her "wisdom, her incredible warmth and grace", as well as her "sharp wit".
"People across the UK - whether they had the good fortune to meet Her Late Majesty or not - will be reflecting today on what she meant to them and the example she set for us all," he added.
Labour leader Sir Keir Starmer said the queues to see the late Queen lying in state showed she "always enjoyed a special bond with her people".
"It was a relationship built from her understanding that service of this great nation is the thread that unites sovereign and subject," he said.
"So, as we reflect on her legacy again today, let us embrace that spirit of public service as our guide towards a better future."
The King has spent the summer at his Birkhall residence and Balmoral Castle in Aberdeenshire.
Gun salutes will be fired at midday on Friday in Hyde Park and at the Tower of London to mark the anniversary of his accession to the throne.
Bells will also be rung at Westminster Abbey at 13:00 BST to mark the occasion.
Prince Harry has separately been paying his own tribute to the late Queen, saying she "is looking down on all of us".
In a speech at the WellChild Awards ceremony in London on Thursday, he recalled how he had been forced to miss last year's event as he flew to Balmoral after his grandmother became ill.
-- Courtesy of BBC Sport