The 18 pages of manuscript, written in 1970-71 in pencil, ink and typescript on 17 sheets, had been expected to fetch between USD 1 and USD 1.5 million at the auction house. Christie's said the buyer was anonymous.
McLean, 69, said he wanted to release the lyrics to help people understand the true meaning of the song, which depicts turbulent upheavals of the latter half of the 20th century.
"It was an indescribable photograph of America that I tried to capture in words and music," he said in February in the Christie's catalog.
The song was initially inspired by his memories of being a paperboy in 1959 and learning of the death of Buddy Holly, it also represents a changing America from the brightness of the 1950s to darker 1960s.
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The phrase "the day the music died" was long known to refer to the 1959 plane crash that killed rock 'n' roll pioneers Buddy Holly, Ritchie Valens and J.P. "Big Bopper" Richardson.
But in an interview with Christie's, McLean revealed the hidden meaning of the song's six verses, over which music enthusiasts had long agonized.
"I was around in 1970 and now I am around in 2015... There is no poetry and very little romance in anything anymore, so it is really like the last phase of 'American Pie'," he added.
McLean also explained the writing process, saying that ages after he had the words "bye, bye miss American pie," the chorus came to him suddenly while out shopping in a pharmacy in Cold Spring, New York.
Some initial ideas were also dropped as the song set the tone for his second album also called "American Pie" and which was a runaway success.
"So it had to be about a lot of subtle things. It had to be about America, nature and loss, and love, and a whole bunch of things, and other things wouldn't fit," he said.