Robin Cook was walking with wife Gaynor when he collapsed
It is believed he was taken ill while walking with his wife Gaynor near the summit of Ben Stack, at around 1420 BST, Northern Constabulary said.
Mr Cook was flown by coastguard helicopter to Raigmore Hospital in Inverness, where he was pronounced dead, said an NHS Highland spokesman.
Mr Cook quit as Commons leader in March 2003, in protest over the war in Iraq.
Following Mr Cook's death, former friends and colleagues paid tribute to him.
The Conservative leader Michael Howard said: "He is a very great loss. He was someone who made an immense contribution to our political life."
Liberal Democrat leader Charles Kennedy said: "Scottish, British and international politics have lost a good and gifted man."
Keen walker
RAF Kinloss Assistant controller Tom Docherty said the centre had received a call about a "collapsed male walker".
Mr Cook was walking near the summit of Ben Stack
"He was given CPR with instructions over the telephone from ambulance control staff at Inverness."
It is understood Mr Cook, who has two adult sons, arrived at hospital at 4pm, about 90 minutes after his collapse and was declared dead five minutes later, said an NHS Highland spokesman.
It was more than three hours before police confirmed his death, as it is believed family members were being informed.
Following Mr Cook's death, a report will be prepared for the Procurator Fiscal, as is usual in such circumstances.
Landslide win
The Livingston MP, who lived in Edinburgh, was a keen walker and cyclist and a keen follower of horse racing.
Robin Cook was flown from Ben Stack to Inverness
He first became an MP for Edinburgh Central in 1974 and was appointed the shadow health secretary in 1989, becoming shadow trade and industry secretary in 1992.
In 1994, he became the shadow foreign secretary, a position he held until the 1997 election.
After Labour's landslide win, he entered the Cabinet as foreign secretary.
A Cabinet reshuffle after the 2001 Labour victory saw him replaced at the Foreign Office by Jack Straw, with Mr Cook instead given the job of Leader of the Commons.
He resigned that position in the lead-up to the conflict in Iraq in protest over Tony Blair's decision to go to war.
He had been an outspoken critic of the government's foreign policy from the backbench.
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.