Marks, from Kenfig Hill, Bridgend county, announced last year he had been diagnosed with inoperable bowel cancer.
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.
The life of 'Mr Nice' Howard Marks
No regrets as Marks lives with cancer
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.

There are currently five drop-in clinics in England for victims of the practice, which affects an estimated 200 million women and girls worldwide.
But there is no such medical provision in Wales.
Now charity Bawso is working to open a pilot clinic at the Cardiff Royal Infirmary to provide medical and psychological help to survivors.
In 2014-15 Bawso supported 788 families affected by FGM in Wales which, according to the World Health Organization involves "the partial or total removal of the female external genitalia or other injury to the female genital organs for non-medical reasons".
Bawso's violence against women director Dr Mwenya Chima said: "In the UK there are women's clinics for women who have had FGM, for medical and psychological help. Survivors can just walk in and ask for help.
"But in Wales we don't have any of that. We are trying to make a case to health agencies that we need to have this kind of clinic, even if it is initially for one day a week for a year to see if there is a demand."
Dr Chima believes there is a big gap in the support provided, and that many survivors of FGM in Wales are not known about.
She said: "I worked with a young women recently - a survivor of FGM - who wanted medical help as she was having problems. Although she wanted help she was already in two minds about having anything done as she was going against her parents.
"We tried to get her help from the clinic in Bristol, but there were delays because she was outside the area, so in the end it didn't happen and she is still living with these problems now."
The call comes as the world marks the international day of zero tolerance to FGM - a UN-sponsored event to raise awareness of the issue.
Although it has been illegal to carry out FGM in the UK since 1985, there have been no successful prosecutions relating to the practice, which is carried out for cultural and religious reasons in certain communities.
Former drug smuggler turned author Howard Marks has died at the age of 70.
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Campaigners want a dedicated clinic for victims of female genital mutilation (FGM) to be opened in Wales.