The 74-year-old British head of state recalled his "great affection" for his mother, her life, and her contributions to society in a brief statement.
He continued, "I am extremely appreciative of the love and support that have been shown to my wife and myself over this year as we try our best to serve you all.
The monarch, who is visiting his Scottish Highland estate of Balmoral, won't be attending any formal engagements on Friday, so there won't be any big celebrations.
He and his wife Camilla will attend nearby Crathie Kirk, the late queen's place of worship, for private prayers and a moment of reflection.
His mother, who was on the throne for a record-breaking 70 years, died at Balmoral at the age of 96 after a period of declining health.
Throughout her reign she did not publicly mark her accession, as it was also the anniversary of her own father King George VI's death in 1952.
Last year, when she began her Platinum Jubilee year on February 6, she spent the day in private at her Sandringham estate in Norfolk, eastern England.
In London, the King's Troop Royal Horse Artillery will mark Charles's accession by firing a 41-gun ceremonial salute in Hyde Park from 12:00 pm (1100 GMT).
Members of the Honourable Artillery Company - the oldest regiment in the British Army - will fire a 62-gun salute from the Tower of London from 1:00 pm.
Both regiments were involved in firing the Death Gun salutes to mark the queen's death, and the Proclamation salutes to mark Charles's new reign.
The king's eldest son and heir, Prince William, and his wife, Catherine, will commemorate the anniversary with a small private service at St Davids Cathedral in west Wales.
William's estranged younger brother, Prince Harry, was in the UK for a charity event on Thursday but was not expected to meet members of his family.