The ex-Army officer, from London, had been rescued 30 miles shy of his goal.
Mr Worsley, 55, was trying to complete the unfinished journey of his hero, Sir Ernest Shackleton, 100 years later, but in his final audio message, he said: “My summit is just out of reach.”
In that last broadcast, sent from Antarctica on Friday, he told supporters: “When my hero, Ernest Shackleton, was 97 miles from the South Pole on the morning of January the 9th 1909, he said he’d shot his bolt.
“Well, today I have to inform you with some sadness that I too have shot my bolt.”
Mr Worsley said his journey had ended because he did not have the ability to “slide one ski in front of the other”.
“I will lick my wounds, they will heal over time and I will come to terms with the disappointment,” he added.
Prince William has led the tributes to Mr Worsley, who was raising money for the Endeavour Fund, a charity which helps wounded servicemen and women and is managed by the Royal Foundation of the Duke and Duchess of Cambridge and Prince Harry.
The duke, who was patron of the expedition, said he and Prince Harry had lost a friend, as he paid tribute to Mr Worsley’s “selfless commitment” to fellow soldiers.
“He was a man who showed great courage and determination and we are incredibly proud to be associated with him,” he said.
The princes pledged to ensure Mr Worsley’s family, which includes his two children, Max, 21, and Alicia, 19, received the support needed “at this terribly difficult time”.