The painter, who was 71, died surrounded by his family following a long spell of ill health.
A picture of a laughing Mr Bellany was posted on the front page of his website. Above the words John Bellany 1942 - 2013, a tribute read: "It is with great sadness that we announced the passing of a true Scottish giant.
"At seventeen minutes past seven on the evening of Wednesday 28th August, John passed away, in his studio, surrounded by his family. He was clutching a paint brush in his hand as he took his final breath.
"His passion was life and he painted as if each day was his last."
News of Mr Bellany's passing had been relayed by text message to some of his closest friends earlier. Within minutes, tributes began appearing on the social networking site Twitter.
Mr Bellany counted David Bowie among his friends and Billy Connolly, Sean Connery and Damien Hirst among his fans, was broken in a text message circulated to some of his friends.
Crime writer Ian Rankin tweeted: "So sad to hear from that John Bellany has died. A painter whose life was as deep and full as the seas he painted."
Mr Bellany's works adorned the walls of galleries the world over, but he had been fighting a formidable list of health problems in recent years.
In 2005, his life was saved through the intervention of a passing nurse when he collapsed in the street. He had suffered a heart attack while heading towards the Mitchell Library, where an exhibition of his work was about to open.
For eight months up to then he had been virtually housebound in the flat he then shared in Edinburgh with his wife Helen after a prolonged bout of pneumonia.
Three years ago it was revealed he was suffering from the condition macular degeneration, which causes loss of central vision, making faces hard to recognise.
As an alcoholic, he was forced to become teetotal after a liver transplant in 1988.
All three of his children, with his eight grandchildren, live within a few minutes' drive of the Bellanys' home near Saffron Walden, Essex.
Known for often dark and nightmarish paintings, as well as works inspired by his fishing village background - he was born in Port Seton, East Lothian, in 1942 into a family of fishermen and boat builders.
Mr Bellany, the first Scottish artist to earn a seven-figure sum for one of his paintings, and Helen Percy, a fellow student, married when still at Edinburgh College of Art. They settled in London, had three children, and when they divorced in the mid-1970s he suffered a nervous breakdown.
After he recovered, he entered a doomed second marriage with Juliet Lister, one of his mature students, a gentle depressive fated to take her own life.
Mr Bellany remarried Helen, whom he first met at Edinburgh College of Art and who is the mother of his three children - Jonathan, Paul and Anya - after Juliet committed suicide, in 1985.
But years of drinking took its toll, although it never impeded his art.
He studied at the Edinburgh College of Art from 1960 to 1965, and later attended the Royal College of Art in London.
His works, which feature fish, demonic sea birds, haunted portraits and religious symbols, hang in the National Gallery, the Tate and the Metropolitan Museum of Art in New York.
Death itself always haunted the vision of Mr Bellany, from fishermen's funerals in Port Seton to a pivotal visit to the Buchenwald concentration camp in the late-1960s, or the paintings he poured out in 2005 in fellow feeling for the tsunami victims in Asia.
Describing his need to paint, Mr Bellany once said: "It's an outpouring. Every day I wake up and I'm filled, I'm buzzing with ideas."
His first solo exhibition was held in 1965 at the Dromidaris Gallery in Holland.
The first artist to have a one-man show at the National Portrait Gallery in London, which featured a portrait of cricketer Ian Botham, in 1986.
In November, last year, he was celebrated by a major retrospective in the Scottish National Gallery, John Bellany: A Passion for Life.