A statement on Marks' website said he died in his sleep yesterday "surrounded by his four loving children."
Born in Wales, Marks studied physics and philosophy at Oxford University before becoming a marijuana smuggler.
He was arrested in 1988 in an operation led by the US Drug Enforcement Administration and sentenced to 25 years in prison. He was released on parole in 1995.
"Mr. Nice" was published in 1996 and made Marks something of a folk hero. He had a column in a men's magazine, toured a one-man show and ran unsuccessfully for Parliament in 1997 on a platform of legalising cannabis.