The $20 coin, known as a double eagle, took less than 10 minutes to sell to a telephone bidder.
The previous record auction price for a coin was just over $4.1m, paid in August 1999 for an 1804 US silver dollar.
The double eagle was minted in 1933, but never went into circulation.
President Franklin D Roosevelt ordered the destruction of all 500,000 of the coins, but one survived and went missing for 60 years.
It was legally on sale for the first time.
The one that got away
The double eagle has been described as the holy grail of coins, and a throwback to the days of the California gold rush.
It was never legal tender.
Under emergency measures to tackle the depression, President Roosevelt - who had just taken the US off the gold standard - ordered all the coins to be melted down.
But when all the gold was weighed, ten coins were found to be missing. All but one were recovered.
At one point the coin was exported to King Farouk of Egypt.
The double eagle surfaced again in the late 1990s when a British dealer tried to sell it to American agents posing as coin collectors at a hotel in New York.
After a five-year legal wrangle, the coin could finally be sold under an agreement between the US Government and the dealer, Stephen Fenton.
This is the only double eagle that a private collector can ever legally own.
It was sold by the coin dealer Stack's and the auction house Sotheby's.
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