Michael O'Grady, 64, from Irvinestown in Northern Ireland, was reported overdue on January 6 after going walking in the area of Ben Alder and Loch Ossian in the Highlands.
He was last seen on December 22 having left the Loch Ossian youth hostel to walk to Culra Bothy.
Lochaber Mountain Rescue Team found the body of a man in the Corrour area to the west of Ben Alder on Saturday, Police Scotland said.
A spokesman said: "Police believe this to be the body of missing climber Michael O'Grady from Northern Ireland, who was reported overdue on January 6."
There appear to be no suspicious circumstances and a report will be prepared for the procurator fiscal.
In a previous appeal to the public police described Mr O'Grady as an experienced hillwalker.