The businessman 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 a fortune through Dennis Publishing, the magazine stable behind Maxim and The Week.
A statement released by his office said he "died peacefully" at his home in Dorsington, Warwickshire, and would be "greatly missed".
His riotous approach to life included spending an estimated $100 million on what he described as "sex, drugs and rock 'n' roll". He also became the first person to say the "c" word on British television.
His foul-mouthed first came during an episode of The David Frost Programme, which included an interview with a group of hippies.
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 made 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.