The prince said that both her and his wife were "deeply saddened" to hear the news of the death of a lady "both of us adored and admired greatly".
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Prince Charles had led the tributes to the Dowager Duchess of Devonshire
"She was a unique personality with a wonderfully original approach to life," Charles said, adding that the Dowager Duchess will "not easily be forgotten".
The Dowager Duchess, known to her friends as Debo, was the last of the Mitford sisters, who both fascinated, and occasionally scandalised, British society in the 1940s.
The most notorious of the siblings were Unity, who was a friend of Hitler, and Diana, the second wife of British fascist leader Sir Oswald Mosley. Jessica was a left-wing activist, and Nancy, a novelist.
The Dowager Duchess of Devonshire was the last of the Mitford sisters
Deborah, like her elder sister Pamela, was more focused on her home life. But during her lifetime she moved in the same circles as Sir Winston Churchill and John F Kennedy, and was painted by Lucian Freud.
Her sister's infatuation with Hitler once saw the young Deborah invited to tea with the German dictator, although he made little impression.
"If you sat in a room with Churchill, you were aware of this tremendous charisma," she later recalled. "Kennedy had it too. But Hitler didn't – not to me anyway."
Debo, as she was known to her friends, pictured in 1954
Born Deborah Vivien Freeman-Mitford on 31 March 1920, the duchess was the sixth daughter of the 2nd Baron Redesdale.
She moved to Chatsworth in the Peak District after marrying Andrew Cavendish, who became the 11th Duke of Devonshire, and proved to have a shrewd business mind; she transformed the house from ruin into a leading tourist attraction - last year Chatsworth attracted more than 600,000 visitors.
The Dowager Duchess of Cornwall with her husband in 1955
Made a dame in 1999, she became the Dowager Duchess of Devonshire in 2004 after her husband died and their son inherited the title.
She is expected to be buried alongside her husband at St Peter's Church on the Chatsworth Estate.