The 78-year-old had been reported overdue by a family member at about 7:30pm yesterday when he failed to return from a walk.
A search was launched and he was found near the summit of Cairn of Barns in the Glen Clova area of Angus last night.
The man from Dundee, who has not been named, had a suspected heart attack.
Officers said he was an experienced hill walker.
A spokesman for Tayside Police said: "Members of Tayside Police search and rescue unit and the Tayside Civilian Mountain Rescue Team attended in the area and quickly located the missing man's vehicle, near to the Glen Clova Hotel.
"The searchers made their way to the Cairn of Barns summit where they traced the hill walker, who was unconscious and suffering from hypothermia.
"He was carried to lower levels and then airlifted to Ninewells Hospital in Dundee. Tragically he died in the early hours of this morning."