Ex-IT professional Andy Norman, 33, from Easthampstead was travelling in the Arctic Circle with two work-mates Philip Goodeve-Docker and Roan Hackney - both from London - when they got caught up in 'Piteraq' a severe wind and snow storm.
The trio had planned to cross the Greenland Ice Sheet from the east to west coast in an "unsupported manner" - the third of the great polar challenges - in aid of Marie Curie Cancer Care, Mind and Age UK.
Both Mr Norman and Mr Goodeve-Docker were first-timers, being led by Mr Hackney who has done several polar expeditions.
They set off on Wednesday, April 24, but on Friday got caught up in the storm and their tent was partially blown away, exposing them to the elements.
Chief Inspector Paul Pitersen of the Greenland Police, which led the rescue, said: "By the time we got to them Mr Goodeve-Docker had frozen to death. The other men are okay and are on their way back to the UK. One has frostbite on his fingers and the other is suffering from shock, but they will both recover."
Before his departure, Mr Norman posted on his Virgin Money sponsorship page: "This is a real deal Arctic expedition - no back-up, no bus to take me away when I'm crying and no warm place to bed down at night. For a month I will be surviving on my own in the Arctic wilderness experiencing some of the harshest conditions on the Earth and trying to avoid polar bears and vast crevices.
"I intend to cover around 400 miles."