Patrick Boothroyd suffered a fall on Ben Nevis on Sunday.
He was airlifted to Belford Hospital in Fort William by the Coastguard but later died from his injuries.
Emergency services were called to the scene of the fall in the Tower Gully area of the mountain at approximately 2.25pm.
A second man was also rescued from the area and taken to hospital, but his injuries are not thought to be life-threatening.
Patrick was from Holmfirth and was studying geology at Cardiff University. He was a former pupil at Greenhead College in Huddersfield. Photos on his Facebook page show him enjoying climbing trips to the Alps, the Dolomites and Greenland.
Mr Boothroyd's family have been informed of his death.
Sergeant Michael Bell said: "Our thoughts are with the man's friends and family at this very sad time.
"There are no suspicious circumstances and a report will be submitted to the Procurator Fiscal in due course.
"I would take the opportunity to thank the crew of the HM Coastguard helicopter and Lochaber Mountain Rescue Team for their assistance with this incident."
In September, a climber from Sheffield died in a cliff fall in the Orkney Islands.