Patrick Boothroyd, from West Yorkshire, was airlifted to Belford Hospital in Fort William by the coastguard.
The 21-year-old Cardiff University student 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.
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.”
Head of Cardiff University’s School of Earth and Ocean Sciences, Professor Ian Hall, said: “Patrick Boothroyd was a diligent, hardworking and well-liked third-year student studying Exploration Geology.
“We are all deeply saddened and shocked by this tragic event. Our immediate thoughts and sympathies are with his family and friends at this extremely difficult time.
“We are encouraging anyone within the University community who has been affected by this tragic event to contact our staff or student counselling services.”