The iconic song - which was released in August 1968 - is one of the Beatles' most popular singles, and according to auction house Julien's Auctions, the lyrics sold for nine times its original estimate in an online auction.
Speaking prior to the sale, Julien's Auctions music specialist Jason Watkins said: "It's obviously a very iconic song that everyone's familiar with.
"These handwritten lyrics were used in the studio as a guide when they were recording it."
Elsewhere, a drawing by John Lennon and his wife Yoko Ono called 'Bagism' sold for $93,750, while an ashtray used by Ringo Starr at the Abbey Road recording studios in London was sold for $32,500.
The auction - which was staged to mark the 50th anniversary of the band's break-up - had initially been due to take place online and at the Hard Rock Cafe in Times Square in New York.
However, it was made an online-only event due to the coronavirus pandemic.
Meanwhile, Paul previously confessed he is incredibly "competitive".
The 'Yesterday' singer always wanted to rise to the top of the music industry - even before he joined the Beatles.
He shared: "I'm competitive with anything.
"We started off in my auntie's back parlour, banging away on three guitars - me, John and George [Harrison] - and we managed to get gigs in Liverpool, and then play the Cavern Club. We were always trying to succeed - I think everyone is."