Biggs, who was 84, was being cared for at the Carlton Court Care Home in East Barnet, North London, died early today.
He had become increasingly frail in recent years after suffering several strokes.
He was last seen in public at the funeral of fellow Great Train Robber Bruce Reynolds in March.
Speaking earlier this year Biggs said he was proud to have been part of the gang behind the robbery.
On August 8, 1963, the robbers, masterminded by Reynolds, stopped the Glasgow-Euston overnight mail train and carried out the biggest robbery of its time.
Biggs escaped from prison in 1965 and spent 36 years on the run before finally being arrested and jailed in 2001.
He was released from prison on compassionate grounds in 2009 due to ill health and subsequently said he had few regrets about the crime that made him a household name.
Biggs, who could not speak due to his strokes and communicated through a spelling board, said: ''If you want to ask me if I have any regrets about being one of the train robbers, my answer is, 'No'.
''I will go further: I am proud to have been one of them. I am equally happy to be described as the 'tea-boy' or 'The Brain'.
''I was there that August night and that is what counts. I am one of the few witnesses - living or dead - to what was 'The Crime of the Century'.''
He did admit to some regrets.
''It is regrettable, as I have said many times, that the train driver was injured,'' he said.
The train driver Jack Mills, who was coshed, reportedly by Biggs, never fully recovered from the ordeal and died a few years later.
Biggs went on: ''And he was not the only victim. The people who paid the heaviest price for the Great Train Robbery are the families. The families of everyone involved in the Great Train Robbery, and from both sides of the track.
''All have paid a price for our collective involvement in the robbery. A very heavy price, in the case of my family.
''For that, I do have my regrets.''
Ronald Arthur ''Ronnie'' Biggs played a minor role in the robbery, in which the gang escaped with £2.6 million, the equivalent of over £40 million today.
Anthony Delano, who wrote a book about the robbery, said Biggs was an "idiot".
"He was a small time south London crook who nobody wanted on the team because he was a weak link."
But his life as a fugitive after escaping from prison gained him notoriety.
He was given a 30-year sentence in 1964, but he escaped after 15 months by fleeing over the walls of London's Wandsworth prison in April 1965.
After having plastic surgery, he lived as a fugitive for 36 years first in Australia then Brazil, where he fathered a son, Michael, who became the key to him being allowed to stay in the country and not face extradition.
Biggs's money ran out and he traded on his notoriety to scrape a living.
His health deteriorated in 2001 and he returned to the UK voluntarily mainly to get the better care available in prison and on the NHS.
He was freed in 2009 on ''compassionate grounds'' by then Justice Secretary Jack Straw, who said he was not expected to recover.
Biggs was last seen in public at the funeral of gang leader Reynolds in London in March when he made a 'V' sign at the waiting press.
Biggs was among 200 well-wishers who paid tribute to Reynolds, who died just months before the 50th anniversary of the infamous heist.
Son Michael, who now lives in England, was not immediately available today but had left a message on his phone saying: "For obvious reasons I'm not taking many calls today."
The Twitter account @ronniebiggsnews, which publicises Biggs' website and autobiography, said: "Sadly we lost Ron during the night. As always, his timing was perfect to the end. Keep him and his family in your thoughts."