The businessman first found fame as one of the founders of 1960s counterculture magazine Oz, which was caught up in a high-profile obscenity trial in 1971.
He went on to make his fortune through Dennis Publishing, the magazine stable behind Maxim and The Week.
Felix Dennis has lost his battle with cancer
A statement released by his office said: "We are deeply saddened to announce that Felix Dennis passed away yesterday surrounded by his loved ones. After a long and painful battle with cancer, Felix died peacefully at his home in Dorsington, aged 67.
"Felix was a publishing legend, famed for his maverick and entrepreneurial style and, more lately, a successful and much-loved poet. He will be greatly missed.
"Thank you for the support and kindness of those who share our feelings for Felix, and we ask that you respect our privacy during our time of grief."
From left: Dennis, Richard Neville and Jim Anderson, the three editors of Oz Publications Inc. Ltd
Dennis's riotous approach to life included spending an estimated 100 million US dollars on what he described as "sex, drugs and rock 'n' roll" and becoming the first person to say c*** on British television.
His foul-mouthed first came during an episode of The David Frost Programme which included a lengthy interview with a group of hippies. He later said his mother refused to speak to him for three years afterwards.
Dennis grew up in the London suburbs and went to Harrow College of Art but left to play in a series of bands which flopped but served as his introduction to the capital's counter-culture.
His involvement with Oz saw him stand trial charged with conspiracy to corrupt public morals after a special issue included a pornographic version of Rupert the Bear.
The trial was a sensation and make Dennis and his fellow defendants famous. They were defended by lawyer and novelist John Mortimer and eventually acquitted on appeal.
Dennis made his millions in publishing where he was a pioneer in the world of computer magazines.
He became a published poet following a life-threatening illness and embarked on a series of book tours and sponsored a prominent poetry prize.
In 2008, he told The Times that he once killed a man by pushing him off the edge of a cliff but later denied the story, claiming he was drunk at the time of the interview.
Dennis, who divided his time between homes in Warwickshire, London, New York, Connecticut and the Caribbean island of Mustique, claimed to have become rich by "accident" and listed his other interests as "planting trees, commissioning bronze sculpture, drinking French wine and avoiding business meetings".