His nephew, Brock Van der Bogaerde, said the former 1950s matinée idol suffered a heart attack at his London home.
He said: "He was extremely happy and looking forward to events like his 80th birthday and many plans for the future.
"I m sure there is not a better way to go."
Bogarde made his acting debut in 1949 and carved out a niche in the 1950s with a succession of romantic leads in dramas and light comedies, among them Doctor at Sea, with a young Brigitte Bardot.
Like Hollywood star Rock Hudson, his sexuality was at odds with his screen persona.
More serious parts
In 1960 the director Joseph Losey gave him a chance to play more serious parts - like The Servant, opposite James Fox.
In Victim, another Losey film, he openly played a homosexual: it was a breakthrough.
Ten years later came perhaps his finest role, working with the Italian director Luchino Visconti on Death in Venice.
He played a dying composer obsessed with a beautiful boy in a city ravaged by cholera.
Bogarde, who anglicised his Dutch surname, relished his fame: in Europe he was revered as an actor as well as a star.
French farmhouse
For 20 years he lived in a farmhouse in Provence, with his close companion Anthony Forwood. It was here he developed a second career, writing novels and an autobiography.
His screen appearances became increasingly rare.
In These Foolish Things he played an exiled Englishman in France, facing death with, as he claimed, no regrets.
By then Bogarde, had reluctantly returned to England - a rather melancholy end for a great star who remained a very private man.
'A unique human being'
Glenda Jackson, the government minister and former actress, said: "I'm desperately sorry that he's died.
"I worked with him and I regarded him as a friend, although I have not seen him for quite some time.
"He was our first home-grown film star - he made some remarkable films."
British film director Michael Winner said Sir Dirk was a "gracious, charming" man and said: "People forget that Dirk Bogarde was the male hero of Britain for about 20 years."
'Di Caprio of his day'
"Every girl in the country was in love with him. He was the UK's Leonardo Di Caprio of his day.
"They don't grow them like that now - it's a very sad day."
A Buckingham Palace spokeswoman said the Queen would be "saddened" to hear of Sir Dirk's death.
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Matinée idol who broke gay taboo
(08 May 99 | Entertainment)
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