Thompson was found shot dead at his home outside the ski resort of Aspen on Sunday night, police said.
"We do have confirmation that Hunter Thompson was found dead this evening of an apparent self-inflicted wound," said Tricia Louthis, spokeswoman for the Pitkin County Sheriff's Office.
Thompson's son, Juan, released a family statement to the Aspen Daily News saying: "Hunter prized his privacy and we ask that his friends and admirers respect that privacy as well as that of his family."
His 1971 book Fear and Loathing in Las Vegas, adapted from an article written for Rolling Stone magazine, chronicled Thompson's drug-hazed misadventures in Las Vegas while covering a motorcycle race.Gonzo journalism
The book established Hunter as a cult celebrity and became the basis for a 1998 Hollywood adaptation, starring Johnny Depp as Thompson's alter-ego, Raoul Duke.
Thompson made his drug and alcohol-fuelled antics and clashes with the authorities the central theme of his work, challenging the conventions of traditional journalism and creating a larger-than-life outlaw persona for himself along the way.
"The oligarchy doesn't need an educated public. And maybe the [American] nation does prefer tyranny"
He dubbed his style of writing "gonzo" journalism and was commonly known as the godfather of that brand of journalism.
He was famous for distrusting power all his life and he believed George Bush's administration had "manufactured" the Iraqi threat for its own political gain as well as the economic gain of what he called the "oligarchy", website salon.com said.
He also criticised the American people for not exercising their right to vote, the website said.
"The oligarchy doesn't need an educated public. And maybe the nation does prefer tyranny," he was quoted as saying. "I think that's what worries me."
Nationwide nervous breakdown
He was quoted as saying 9/11 had caused a "nationwide nervous breakdown" and "let the Bush crowd loot the country and savage American democracy", according to an interview published by salon.com in February 2003.
Thompson, who regarded himself as a patriot, said civil liberties had been compromised for what he called "the illusion of security".
That, he said was "a disaster of unthinkable proportions" and "part of the downward spiral of dumbness" he believed was plaguing the country.