Jailed in the US in 1990 after being convicted of smuggling cannabis, he recalled his exploits in a best-selling autobiography, Mr Nice, which was later made into a film starring Rhys Ifans.
The father of four stood for election to Parliament in 1997 on a single-issue ticket of reforming cannabis laws.
Marks also regularly toured a one-man show in which he recounted stories about drug smuggling and his time in prison.
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A statement said: "In the early hours of 10th April 2016, Howard Marks died peacefully in his sleep surrounded by his four loving children.
"He fought the illness with grace and humour.
"His death was 21 years to the day since his release from prison in the United States, his second bout of imprisonment for cannabis smuggling since his miraculous acquittal at the Old Bailey in 1980.
"One of his last acts was to set up the Mr Nice foundation, to ensure the causes dear to him continue to receive his support."
Revealing his illness in January 2015, Marks said he had "no regrets" about his life.
His drug smuggling began in the 1970s after he graduated from Oxford University with a degree in physics.
In 1988, he was arrested in Spain as part of a US Drug Enforcement Agency-led operation and extradited to Florida. He was sentenced to 25 years in prison and released on parole in 1995 for good behaviour.
As well as the film version of Mr Nice, Marks had cameo roles in the movie Human Traffic and appeared on TV including on the BBC quiz show Never Mind the Buzzcocks.
He also collaborated on songs with the Super Furry Animals and made appearances at the Glastonbury festival.
A sequel to Mr Nice, Senor Nice, came out in 2006, and five years later Marks published a crime novel, Sympathy for the Devil.
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