"I can confirm that Anthony died this morning," said a spokeswoman for Minghella's agent Judy Daish Associates.
She said she was unable to provide any details of how he died at this stage.
The writer and director, whose other box office hits include "The Talented Mr. Ripley" and "Cold Mountain," was best known for beautifully shot and lyrical adaptations of literary novels starring big name actors such as Jude Law.
Fellow director Lord David Puttnam said the death was a "shattering blow" to the industry.
He said he was "a storyteller in the classic British tradition."
Minghella won the best director Academy Award for "The English Patient", starring Ralph Fiennes and Juliette Binoche and based on Michael Ondaatje's novel of the same name.
He was also awarded an Oscar for best screenplay writing on the film.
His next film, "The Talented Mr. Ripley", based on a thriller by Patricia Highsmith, starred Jude Law and Matt Damon and earned him a second best screenplay writer award in 1999.
Minghella was born to parents of Italian origin who had an ice-cream shop on the Isle of Wight in southern England.
After studying and teaching at Hull University in northern England, he worked in television before directing the work which first made him a household name in Britain -- "Truly, Madly, Deeply" in 1991.
First shown on television, the tear-jerking drama starred Alan Rickman and follows a woman's relationship with the ghost of her dead boyfriend.
The film drew attention from Hollywood and led to "The English Patient", set during the Second World War, which made him a major player stateside.
That was followed by "The Talented Mr. Ripley" and "Cold Mountain" in 2003, which, despite an all-star cast including Law, Nicole Kidman and Renee Zellweger, received mixed reviews from critics.
He returned to his British roots with 2006's "Breaking and Entering", starring Law as a London architect who has an affair with a Bosnian woman.
Minghella had recently directed a television episode of the Alexander McCall Smith book "The No. 1 Ladies' Detective Agency," which is due to be screened in the next couple of weeks on the BBC.
He had also directed opera and a party political broadcast for Britain's Labour Party featuring then prime minister Tony Blair and his successor, Gordon Brown.
He was chairman of the British Film Institute at the time of his death and was made a CBE (commander of the British empire) by Queen Elizabeth II in 2001.

Copyright AFP (Agence France-Presse), 2008