The 1895 artwork - a modern symbol of human anxiety - was sold at Sotheby's. The buyer's name was not released. The price includes the buyer's premium, an additional amount the buyer pays the auction house.
The image of a man holding his head and screaming under a streaked, blood-red sky is one of four versions by the Norwegian expressionist painter. The auctioned piece at Sotheby's is the only one left in private hands.
The previous record for an artwork sold at auction was $106.5 million for Picasso's "Nude, Green Leaves, and Bust," sold by Christie's in 2010.
The image has become part of pop culture, "used by everyone from Warhol to Hollywood to cartoons to teacups and T-shirts," said Michael Frahm of the London-based art advisory service firm Frahm Ltd.
"Together with the Mona Lisa, it's the most famous and recognized image in art history," he added.
A buzz swept through the room when the artwork was presented for auction as two guards stood watch on either side. Bidding started at $40 million with seven buyers jumping into the competition early.
The battle eventually boiled down to two phone bidders as the historic hammer price was finally achieved after more than 12 minutes.
Sotheby's said the pastel-on-board version of "The Scream" is the most colorful and vibrant of the four and the only version whose frame was hand-painted by the artist to include his poem, detailing the work's inspiration.
In the poem, Munch described himself "shivering with anxiety" and said he felt "the great scream in nature."
Norwegian businessman Petter Olsen, whose father was a friend and patron of the artist, said he sold the piece through Sotheby's because he felt "the moment has come to offer the rest of the world the chance to own and appreciate this remarkable work."
Proceeds from the sale will go toward the establishment of a new museum, art center and hotel in Hvitsten, Norway, where Olsen's father and Munch were neighbors.
The director of the National Museum in Oslo, Audun Eckhoff, says Norwegian authorities approved the Munch sale since the other versions of the composition are in Norwegian museums. One version is owned by the National Museum and two others by the Munch Museum, also in Oslo.
Sotheby's said a total of eight works have sold for $80 million or more at auction.
Only two other works besides Picasso's "Nude, Green Leaves, and Bust" have sold for more than $100 million at auction. Those are Picasso's "Boy With a Pipe (The Young Apprentice)" for $104.1 million in 2004 and Alberto Giacometti's "Walking Man I" for $104.3 million in 2010.
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