The number plate KMT 499C was removed from an Aston Martin DB5 once owned by the late Beatle.
It is part of a collection of rare Harrison memorabilia being sold by Wiltshire-based auctioneers Gardiner Houlgate at its June specialist guitar and music sale.
Also included are a series of letters written by the guitarist, his sister and his sister-in-law.
The number plate is believed to have been taken off the car by a mechanic at Arnold G. Wilson Limited's Regent Street dealership in Leeds in the early 1970s.
It was one of two plates being replaced with new style reflective plates while the car was being serviced.
The rear number plate remained at the dealership for several years until a member of staff sold it to a local barber, who collected car memorabilia, in return for free haircuts for life.
The number plate was subsequently sold to the collector.
The front number plate is known to have hung on the wall of an famous Leeds pub, the Cherry Tree, for many years.
The pub has since been demolished.
Harrison's 1964 Aston Martin DB5 itself was sold at auction in 2011 for £350,000 to an anonymous Beatles fan from Houston, Texas.
Also included in the collection is a letter from Harrison to a fan written on the very day that the Beatles' fourth single She Loves You was released in 1963.
Drafted on headed notepaper from the Palace Hotel, Bournemouth, where the Beatles were staying, the letter reveals that Harrison sings the wrong words on the single's B-side I'll Get You.
Over three pages, Harrison also explains that the group were annoyed at being pelted with Jelly Babies sweets while performing live and that drummer Ringo Starr was too scared to sing on stage, even though Harrison and Paul McCartney offered to play the drums for him.
In addition to books and programmes, the collection also includes letters to Beatles fans written by Harrison's sister, Louise Harrison, and his sister-in-law, Irene Harrison.
The George Harrison memorabilia is being sold by a private collector from Salisbury in order to raise funds for retirement.
Auctioneer Luke Hobbs said: "This is a treasure trove of George Harrison memorabilia including correspondence, programmes and personal belongings.
"I've not seen anything like it before. We're expecting strong international interest, particularly from America.
"It's very hard to estimate what the number plate will fetch as it's never been offered for sale before. As the car it came from sold for £350,000, the plate itself easily make four figures.
"The letter written from Bournemouth in 1963 is an intimate snapshot of the young Beatle, right on the brink of major fame.
"It could go as high as £10,000 to £20,000."
In September last year, Gardiner Houlgate sold Harrison's Maton Master Sound MS-500 guitar for £347,000.
The auction will take place at the auction house in Corsham, Wiltshire on June 12 and 13.