Mr Harvey died on Saturday morning at a hospital in San Francisco, surrounded by family, Burning Man Project chief executive Marian Goodell said.
The cause was not immediately known but he suffered a stroke earlier this month.
Longtime friend Stuart Mangrum posted on the organisation’s website that Mr Harvey did not believe in “any sort of existence” after death.
“Now that he’s gone, let’s take the liberty of contradicting him, and keep his memory alive in our hearts, our thoughts, and our actions,” Mr Mangrum wrote. “As he would have wished it, let us always Burn the Man.”
Burning Man takes place annually in northern Nevada’s Black Rock Desert.
The week-long festival attracts 70,000 people who travel to a dry lake bed 100 miles east of Reno, where temperatures can routinely reach 37.8C during the summer.
There they must carry in their own food, build their own makeshift community and engage in whatever interests them. On the gathering’s penultimate day, the giant effigy – or man as it is known – is set ablaze.
Friends and family toasted Mr Harvey on Saturday as a visionary, a lover of words and books, a mentor and instigator who challenged others to look at the world in new ways.
“Burners,” as they are called, left comments on the organisation’s website thanking him for inspiring them as artists and for creating a community.
“Thanks for everything. (No, really, pretty much everything in my life right now is a result of Burning Man),” read one post.
While tickets now sell out immediately, Mr Harvey described in a 2007 interview how he had much more modest intentions when he launched Burning Man on San Francisco’s Baker Beach in 1986.
“I called a friend and said, ‘Let’s go to the beach and burn a man,” he told the website Green Living. “And he said, ‘Can you say that again?’ And I did and we did it.”
It was not until afterwards, Mr Harvey recalled, that he had the epiphany that led to Burning Man.
Within a few years the event had outgrown Baker Beach and moved to the desert.
While Mr Harvey would speak frequently about Burning Man in the years that followed, he would reveal little about himself and it was often hard to discern truth from fiction.
He believed he was conceived in the back of a Chevrolet by parents who abandoned him soon after his birth, he once told the Reno Gazette-Journal.
His brother, Stewart Harvey, said in a post on Saturday that the two were adopted by farmers Shorty and Katherine Harvey, and grew up outside of Portland, Oregon. The brothers, who were not related by blood, were extremely close.
After that first fire in 1986, Burning Man flourished as Mr Harvey meticulously oversaw its every detail from the various communities that would spring up overnight to its annual arts theme to the beautifully crafted temple that accompanies Burning Man and is also burned.
He eventually formed a limited liability corporation to put on Burning Man, converting it in 2013 to a nonprofit with 70 employees and a budget of $30m (£22m). He was president of its board and chief philosophic officer".
Although known for retaining its joyful atmosphere as it grew from a small gathering to one of gigantic proportions, Burning Man occasionally had its problems.
In 2017, a man ran into Burning Man's flames, suffered burns over almost all of his body and died. In 1996, three people were injured when a drunken driver ran over their tent. That same year a man was killed when his motorcycle collided with a van carrying people to the festival.
In 2007, a prankster set fire to Burning Man four days early and it had to be frantically rebuilt while the man was charged with arson.
He is survived by his son Tristan Harvey; brother Stewart Harvey; and nephew Bryan Harvey.
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