The renowned photographer and film maker died peacefully at his home on Friday, according to his picture agency Camera Press.
Lord Snowdon married Princess Margaret on 6 May 1960 but they separated after 16 years of marriage and the divorce was finalised in 1978.
Buckingham Palace said the Queen had been informed.
BBC royal correspondent Nicholas Witchell said the Queen was "saddened" by the news of his death. He added that Lord Snowdon had been ill for some time.
Snowdon, born Antony Armstrong-Jones, photographed famous faces including Diana, Princess of Wales, Jack Nicholson, Elizabeth Taylor and David Bowie during his career.
He also worked in design, co-creating an aviary for London Zoo and inventing an electric wheelchair.
He was married twice, to Princess Margaret for 18 years and to BBC researcher Lucy Mary Lindsay-Hogg between 1978 to 2000.
He began his career as a society photographer for Tatler magazine in 1952, meeting Princess Margaret through his work.
ord Snowdon was a talented film maker and photographer whose marriage to Princess Margaret fed the gossip columns for more than a decade.
His career was punctuated by lurid tales of extra-marital affairs, alcohol and drugs, but throughout it all he maintained a close contact with the Royal Family.
His body of photographic work featured the cream of British society, although he was usually dismissive about his work.
He was most proud of the stunning aviary he helped design for London Zoo.
He was born on 7 March 1930 into a family of minor gentry.
Ingrid Seward, editor of Majesty Magazine, told BBC News Lord Snowdon and Princess Margaret had been at the heart of an "extraordinary period of glamour" for the royal family.
"They hung out with the Beatles, they hung out with Peter Sellers," she said. "It was very avant-garde."
Ms Seward, a royal biographer, said Snowdon was "extremely sad" when his marriage with Princess Margaret ended but that he had "remained friendly" with the royal family until his death.
The Snowdon Trust, the charity that gives grants to disabled students founded by Snowdon in 1981, said its thoughts were with his family.
"He helped change attitudes towards disability and campaigned tirelessly against discrimination," it said.
Snowdon was the son of barrister Ronald Armstrong-Jones QC and Anne Messel, who went on to become the Countess of Rosse.
He was educated at Sandroyd School, Salisbury, and then Eton, before heading to Jesus College, Cambridge, to study natural history.
He switched to architecture after only 10 days but he eventually embarked on a career as a photographer after failing his second year exams.
During his career he also photographed actors and actresses for theatre publicity shots, including Laurence Olivier and Marlene Dietrich.
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