Patrick Boothroyd, from West Yorkshire, was airlifted to Belford Hospital in Fort William by the coastguard.
The 21-year-old 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.
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.”