"My father is now a free man and that's all there is to say.
"It was very emotional when the guards left."
Michael Biggs said a duty prison governor outlined the terms and conditions of the release on licence to his father.
He waved the paperwork and told journalists: "It smells like freedom."
He added: "My father still has a sense of humour, he shook hands with the prison guards and then just waved them off with his hands."
He said earlier that his father was unable to walk, read, write or speak and could not eat or drink.
Michael Biggs added: "The media made Ronnie Biggs into what he is and the media is here when Ronnie Biggs is about to close this last chapter. He will now be retreating fully from public life."
Michael Biggs thanked a number of people including Mr Straw and added: "There is a God and maybe he is Anglo-Brazilian."
Michael Biggs said his daughter Ingrid, nine, was hoping to visit her grandfather later.
Hospital officials said Biggs' treatment would not change.
They said he would remain on a general ward with other elderly patients until he was deemed fit to leave by doctors.
Biggs 'not deserving of forgiveness'
Peter Rayner, a former chief operating officer for British Rail who worked with Jack Mills - the train driver injured in the 1963 robbery, said: "One can't forget and one has to be clear that driver Mills... died as a result of injuries from criminals.
"Driver Mills was a man who stood against those criminals and said he wouldn't move his train with its valuable cargo.
"Driver Mills paid the penalty in that. So my feeling is one of concern that the perpetrators have been treated as folk heroes rather than the criminals that we on the railway believe them to be."
Last month, Mr Straw said Biggs should not be granted parole as he remained "wholly unrepentant" about his involvement in the 1963 robbery of a mail train.
But on Thursday Mr Straw said the medical evidence clearly showed "that Mr Biggs is very ill and that his condition has deteriorated recently".
He added: "His condition is not expected to improve. It is for that reason that I am granting Mr Biggs compassionate release on medical grounds."
The former Norwich Prison inmate, who was serving a 30-year sentence, was taken to hospital in June suffering from a chest infection and was readmitted on Tuesday.
His son added: "I'm just very hopeful that my father can have another few months ahead of him in his life."
The decision means Biggs will spend his 80th birthday on Saturday as a free man.
If his condition improves Biggs will be transferred to a nursing home in Barnet, north London, near his son's home.
Biggs, originally from Lambeth, south London, was a member of a 15-strong gang which attacked the Glasgow to London mail train at Ledburn, Buckinghamshire, in August 1963, and made off with £2.6m in used banknotes.
The train's driver, Jack Mills, suffered head injuries during the robbery.
Biggs was given a 30-year sentence, but after 15 months he escaped from Wandsworth prison, in south-west London, by climbing a 30ft wall and fleeing in a furniture van.
He was on the run for more than 30 years, living in Australia and Brazil, before returning to the UK voluntarily in 2001 in search of medical treatment.
He was sent to Belmarsh high-security prison on his return before being moved to a specialist medical unit at Norwich Prison.
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