Two Nottinghamshire climbers were airlifted from Stob Coire nan Lochan, part of the Three Sisters ridges in Glencoe, on Saturday March 9.
They were found at about mid-day, both with hypothermia, after they were reported overdue from a climb the previous day.
The climbers, aged 57 and 47, were found following an extensive search involving police, HM Coastguard and mountain rescue teams.
Police Scotland said the 57 year old man, who was being treated at Aberdeen Royal Infirmary, had died, and that his family have been informed.
A statement released on Sunday, March 10 said: "Police Scotland can confirm that one of the two missing climbers rescued from the Glencoe area on Saturday has sadly passed away."
The second climber remains in a stable condition at Belford Hospital in Fort William.
The search began on Friday evening and resumed at 8am on Saturday, involving Glencoe, Lochaber and Oban Mountain Rescue Teams and a Coastguard helicopter.
Oban Mountain Rescue Team released a statement following his death, that read: "Unfortunately, it has just been announced that one of the gentleman we helped to rescue yesterday in Glencoe did not survive his injuries. Our thoughts are with his family and friends."
After the climbers were rescued on Saturday,a spokesman from Glencoe Mountain Rescue said: "When the rescue resumed on Saturday Team were planning for an avalanche search and as is normal practice called for assistance from our neighbouring teams.
"We would like to thank Arrochar MR, Lochaber MR, Oban MR, RAF MR, Police Scotland MR, SARDA, Coastguard helicopter crews and our local ambulance crew.
"We would also like to thank two climbing parties who were on the hill on Saturday and who dropped their plans for the day to help and who played an important part in the rescue.
"Finally we would like to thank the Team at Clachaig, who took us all in, fed and watered us when the rescue had concluded."