Mr Cook had apparently collapsed with a suspected heart attack on the mountainside while out walking during his summer holidays.
He was also reported to have seriously injured himself in a fall after his collapse.
The father-of-two grown up sons was on the mountain for nearly half an hour before rescue services reached him.
Then, guided by medical experts via telephone, they battled to revive him using cardio pulmonary resuscitation equipment, before he was airlifted by helicopter to hospital in Inverness.
But it was more than three hours later before police confirmed his death.
A police spokesman added: "As is normal in such circumstances, a report will be prepared for the Procurator Fiscal."
Prime minister Tony Blair described Mr Cook as "an outstanding, extraordinary talent".
In a statement released by 10 Downing Street, Mr Blair said: "Our thoughts and prayers are with Gaynor and all Robin's family.
"This news will be received with immense sadness, not just in Britain but in many parts of the world.
"Robin was an outstanding, extraordinary talent - brilliant, incisive in debate, of incredible skill and persuasive power."
Mr Cook was a keen hill-walker, who regularly spent his summer holidays with close family and friends enjoying the dramatic mountain scenery of Highland Scotland, rather than going abroad.
A leading figure in the Labour party for decades, Mr Cook was put in the key job of foreign secretary when the party won power in 1997.
He was demoted to the post of leader of the Commons following Labour's second election victory in 2001 and resigned from the cabinet in protest at the Iraq war in 2003.
He then became one of the sharpest critics of the government's foreign policy in Iraq.
Mr Cook's devotion to enhancing the role of parliament as leader of the Commons made him a popular figure among backbench MPs, and his powerful resignation speech on the eve of war won him great respect from opponents of military action.
Robin Cook
Robin Cook, the former British foreign secretary and current Member of Parliament, has died of a suspected heart attack after collapsing on a walk with his wife on Ben Stack hill, Scotland. Cook, aged 59, was flown to a hospital in Inverness by a rescue service helicopter half an hour after collapsing. 

A spokesperson for NHS Highland said that Mr. Cook arrived at hospital 90 minutes after his collapse, and was reported dead five minutes later. A postmortem examination has concluded that he died from hypertensive heart disease.

Mr. Cook was buried on August 12 at St Giles Cathedral in Edinburgh in a service attended by close family, friends and political figures from across the world. British Prime Minister Tony Blair however came under attack from Mr. Cooks friend and racing pundit John McCririck for his absence from the service.  

Robin Cook served as Foreign Secretary under New Labour and was a critic of the war in Iraq. He  resigned as Leader of the House of Commons in 2003 in protest against Prime Minister Blair's foreign policies.