He left for a walk with his brother Neil, 63, at around 7.45am on Thursday from Strathcarron - five miles from where his body was found.
Search-and-rescue teams found Alan Gibson's body, and police have notified his family.
Alan Gibson, 56, had not been seen since setting out with his brother, Neil Gibson, 63, and their dog on Thursday morning.
One of the brothers was thought to have travelled to the Wester Ross area from County Durham, while the other came from Nairn.
The body of one of two walkers reported missing in the Scottish Highlands has been discovered by mountain rescue teams.
The search is continuing for Mr Gibson's brother Neil, who went hillwalking with him in the Achnashellach area of Strathcarron in Thursday.
A police spokesperson said: "The family of Alan have been informed and our thoughts are with them at this very sad time".
Mountain rescue teams from Kintail, Torridon and the RAF have been searching the peaks of Fuar Tholl, Sgorr Ruadh and Beinn Liath Mhor.
Police urged anyone who remembers seeing the men or has information about their whereabouts to contact them on 101 quoting reference 4089 of 8 February.
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