Noble Grossart bank confirmed its chief executive passed away peacefully at home on Friday with his family by his side.
First Minister Nicola Sturgeon paid tribute to him following news of his death.
She said: “I am deeply saddened to hear news of the passing of Sir Angus Grossart – a titan of the Scotland’s business community.
“Through his significant contributions to the arts, culture, the economy and public life, Sir Angus leaves a deep and lasting legacy.
“I want to pay particular tribute to the work of Sir Angus in his years of public service including leading the National Museum of Scotland, the National Galleries of Scotland and the Scottish Futures Trust.
“I extend my sympathy to Gay and to her family at this sad time.”
Noble Grossart Limited is a merchant bank which was formed in 1969 and advises many leading Scottish companies, institutions and private companies.