The instrument - a 1959 Martin D-18E - was played by the late musician during a special Nirvana concert in November 1993, five months before Cobain died at the age of 27.
The seventh of only 302 D-18Es built by Martin, the guitar had also been customised by Cobain, who added a Barolini pickup to the soundhole.
The piece went up for sale by auction, with Julien's Auctions opening the bidding at $1 million.
The price soon rocketed, with the auction closing on a winning bid of $6,010,000 from Australian businessman Peter Freedman, who founded RØDE Microphones.
He plans to display his costly purchase in a global exhibition tour, taking it to galleries and art spaces around the world and giving all proceeds to the performing arts.
Freedman, whose family first opened an electronics shop in Sydney in 1967, admitted he was 'scared s***less and shaking' when he won the auction, but feels proud that he'll be able to use the guitar to help others.
"It's a big deal," he told the Press Association.
"I didn't even buy it for me. I paid for it but I'm going to use it to highlight the plight of artists worldwide by touring it around and then I'm going to sell it and use the dough for that as well, later."
Freedman continued: "The musicians and artists have supported my family since the 60s. We've been in that game forever so I've been very lucky with Rode and I've been able to give away lots of money, quite a few mill."
According to Julien's Auctions, the incredible sale set five world records, including most expensive guitar and most expensive piece of memorabilia.
But Freedman said he had no limit on what he would have paid, adding: "There were some seriously rich people here and I suppose I could have been completely scared s***less and somebody who has got billions and billions just pays, what, 20, 30 million? But I would have kept going."
In a post on the RØDE Microphones website, Freedman also said: "The global arts industry has been shattered by the impact of COVID-19, with musicians and artists being amongst the most affected. The last few months were the straw that broke the camel's back, and for many in the arts have brought forth the harsh reality that they work in an industry for which there is little support in times of need.
"For most, access to financial and health services - particularly mental health services - is very limited. While many industries are gradually returning to normal, it's going to take a long time before this industry can begin functioning as it was. The toll this has taken and will continue to take is enormous and requires more than just lip service. It requires action now, and I am a man of action.
"The arts, and organisations that support the arts, are remarkably undervalued and underfunded by many governments around the world, considering their cultural and economic importance.
"I saw buying this guitar as an opportunity to not only share it with music fans, but to do so in a way that raises awareness for the struggles that musicians and artists face every day, and lobby governments for change."
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