That's more than 8,000 times what then-NASA intern Gary George paid for them in a government surplus auction in 1976, the auction house said in a news release.
The videos have not been restored, enhanced or remastered, and are the "earliest, sharpest, and most accurate surviving video images of man's first steps on the moon," Sotheby's said.
"Fifty years ago today, we achieved the world's greatest human accomplishment, and what we universally recall about that event is best documented on these tapes," said Cassandra Hatton, vice president and senior specialist in Sotheby's Books & Manuscripts Department, said in a release. "We are truly over the moon about today's outstanding result."
The auction house didn't say who bought the recordings.
The tapes contain the images shown the world over: Neil Armstrong's first step, Buzz Aldrin descending the ladder after him and bouncing over the moon's surface, and the astronauts planting the American flag there, but the images are "sharper and more distinct" than those shown elsewhere, Sotheby's said.
The footage shown on network television broadcasts lost video and audio quality with each transmission from microwave tower to microwave tower, Sotheby's said.
George was an engineering student at Lamar University when he interned at the NASA Johnson Space Center and occasionally went to government surplus auctions, Sotheby's said. In June 1976, he paid $217.77 for a lot of about 1,150 reels of magnetic tape that had belonged to NASA.
George sold and donated some of the tapes, but he saved three of them after his father noticed they were labeled "APOLLO 11 EVA | July 20, 1969 REEL 1 [--3]" and "VR2000 525 Hi Band 15 ips." He didn't give them much thought until he found out in 2008 that NASA was trying to locate its original tapes for the 40th anniversary of the moon landing, Sotheby's said.
The tapes have a combined run time of 2 hours and 24 minutes, and they show the entirety of the moon walk as seen by the Mission Control staff, from the first walk to the phone call with then-President Richard Nixon, the auction house said.