The original document is now going on sale on the music memorabilia website Gotta Have Rock and Roll, where it is expected to go for $40,000 (£33,000).
The handwritten three-page letter was penned by the “Imagine” singer in November 1971.
It was written 18 months after the band split, and in it Lennon comments on McCartney suing The Beatles and a recent interview he had done with Melody Maker magazine.
Addressing “my obsessive old pal”, Lennon writes that “it’s all very well playing ‘simple, honest ole’ human Paul’ in Melody Maker, but you know damn well we can’t just sign a bit of paper”.
“If you’re not the aggressor (as you claim), who the hell took us to court and s*** all over us in public?” Lennon writes. “As I’ve said before – have you ever thought you might possibly be wrong about something?”
He also disagrees with McCartney’s claim that “Imagine” “ain’t political”, writing: “You obviously didn’t dig the words… Your politics are very similar to Mary Whitehouse’s – ‘saying nothing is as loud as saying something!’
Lennon ends the letter: “No hard feelings to you either. I know we basically want this same, and as I said to you on the phone and in this letter, whenever you want to meet, all you have to do is call.”
In an interview last year, McCartney said that he still blames Lennon for The Beatles splitting.
“I didn’t instigate the split. That was our Johnny,” McCartney said. “This was my band, this was my job, this was my life, so I wanted it to continue.”