The ex-Army officer, 55, was 30 afar abbreviate of his ambition of acceptable the aboriginal being to cantankerous the abstemious unaided.
In a statement, his wife Joanna said she acquainted "heartbroken sadness". Mr Worsley, from Fulham in London, died of "complete agency failure", she added.
The Duke of Cambridge said he was "very sad" to apprehend of Mr Worsley's death, while David Beckham aswell paid tribute.
"He was a man who showed abundant adventuresomeness and assurance and we are abundantly appreciative to be associated with him," Prince William said.
In a bulletin appear afore he was airlifted to Chile for treatment, Mr Worsley wrote: "The 71 canicule abandoned on the Antarctic with over 900 statute afar covered and a bit-by-bit cutting down of my concrete ability assuredly took its assessment today, and it is with anguish that I address it is journey's end - so abutting to my goal."
The ReMark Group, which was acknowledging Mr Worsley's effort, said in a statement: "When Henry was best up by Antarctic Logistics and Expeditions (ALE), he was adversity from burnout and dehydration.
"He was aureate to a hospital in Punta Arenas [in Chile] area he was begin to accept bacterial peritonitis.
"This resulted in Henry ability anaplasty but in animosity of all the efforts of ALE and medical staff, he succumbed."
Peritonitis is deepening of the peritoneum, the attenuate band of tissue that curve the central of the abdomen. According to the NHS, a lot of cases appear from abrasion or infection in addition allotment of the body.
On Instagram, David Beckham said he was "lucky to accept met Henry", who had "served our country for so abounding years".
And charlatan Bear Grylls tweeted: "We are devastated by this loss. One of the arch men & bravest soldiers I know. Praying for his appropriate family."
Mr Worsley began the 1,100-mile (1,770km) coast-to-coast expedition in November, affairs a sledge absolute his food, covering and equipment.
The plan was to cantankerous the abstemious "unassisted and unsupported" - with no accumulation drops or advice from dogs or any added source.
He had anesthetized his ambition of adopting £100,000 for the Endeavour Fund, which helps afflicted and ailing servicemen and women.
In a statement, the armamentarium said it was "devastated" by account of Mr Worsley's death.
'Drive' for soldiers
In October, he told the BBC he accepted to lose two rock (12.7kg) during the challenge.
He said his adventure should yield 75 canicule and he would yield abundant aliment for 80 days, adding: "I could accomplish it endure a bit longer."
Asked if he was "mad" to yield on the challenge, he said: "There is no atramentous art to sliding one ski in foreground of the other.
"What will drive me on is adopting money for these blood-soaked soldiers."
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