"We owe her the most heartfelt debt any family could owe to their mother for her love, affection, guidance, understanding and example," he said.
King Charles, 73, also acknowledged the "personal grief that all my family are feeling" as they join their country in mourning the death of a monarch who was also a mother and grandmother to his sons, Prince William and Harry.
"This is a time of change for my family," Charles continued in his inaugural address to the kingdom which he recorded in the Blue Drawing Room of Buckingham Palace, where Queen Elizabeth delivered Christmas remarks to her subjects over the years.
As his heir, William assumes the titles Charles held before Elizabeth's death, becoming the Duke of Cornwall and Prince of Wales, the king announced on Friday.
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King Charles also acknowledged his younger son, the Duke of Sussex, who is now fifth in line to the throne. Harry's children with wife Meghan Markle, Archie Mountbatten-Windsor and Lilibet Mountbatten Windsor, are now sixth and seventh in line, respectively.
"I want also to express my love for Harry and Meghan as they continue to build their lives overseas," the king said.
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Harry and Meghan, who live in California with their children, have been in the U.K. this week to carry out a series of charity visits. On Thursday, Harry traveled to Scotland to join his family in mourning the loss of his beloved grandmother.
The Duke of Sussex, 37, returned to Windsor Friday after spending the night at Balmoral, according to his spokesperson. He and Markle, 41, will remain in the U.K. until his grandmother's funeral.
Markle did not join her husband in Scotland. The couple was scheduled to attend the WellChild Awards in London on Thursday — where Harry was due to give a speech — but they canceled their appearance after news of the Queen's declining health broke early on Thursday.