Angus Douglas-Hamilton died at his home in East Lothian on Saturday at the age of 71.
His wife, Kay Hamilton, a passionate animal rights campaigner, paid tribute to her husband as a "wonderful, fun and loving man".
She said: "Over the last few days he had become increasingly ill and we knew that time was running out. He died peacefully in the early hours of Saturday morning in my arms in the comfort of our home."
The Hamilton dukedom is the oldest in Scotland, dating back to the mid-17th century.
The 15th Duke of Hamilton was born in London in 1938 and was the eldest son of the 14th Duke. He was educated at Eton and Oxford.
In his younger days he was a keen flyer and car-racer.
He was the Hereditary Keeper of the Palace of Holyroodhouse, the Queen's official residence in Scotland.
He could trace his ancestry back to Mary Queen of Scots and was custodian of the family's 14th-century seat, Lennoxlove House in East Lothian.
The Duke was hereditary bearer of the Crown of Scotland to the Parliament of Scotland, so had the honour of carrying the Crown in front of the Queen at the opening ceremony of the Scottish Parliament.
The duchess recalled the moment he nearly dropped it.
"He was walking with the crown on a cushion and as he came down some steps he almost lost his footing and was about to shout out to his friend the Lord Lyon, 'Here, catch', but he swallowed his words when he realised the Queen was right behind him."
The Duke was diagnosed with dementia in 2001. But the duchess said: "Even though the dementia made things difficult we still had fun together."
She pledged to continue her long-running campaign for people with dementia to be treated by specialist nurses in hospitals.
Both the duke and duchess have been active animal rights campaigners over the years, banning hunting on their Lennoxlove estate in East Lothian and boycotting Jenners until it stopped selling pat de foie gras.
The duchess said: "I will carry on with the animal rights work that we were both so passionate about."
The Hamilton title will now pass to their eldest son, Alexander Douglas Hamilton, Marquess of Douglas and Clydesdale, who was born in 1978.
A spokesman for Buckingham Palace said: "The Queen is sending a personal message of sympathy to the family."