The instrument attracted worldwide interest and bids from America and Dubai were made.
However, the Gibson UB3 was sold to a man living in the UK by Hansons Auctioneers in Etwall, Derbyshire.
The banjolele was last sold privately in 1972, when late Formby fan Terence Wallin paid £310 for it.
It was originally purchased in 1961 from Formby's estate by Bill Logan, the first president of the George Formby Society.
Auctioneer Charles Hanson said a round of applause echoed around the room as it was sold.
"It was a great honour to handle it. It was quite a moment," he added.
"The room gave a round of applause. It's memories, as an auctioneer, you don't forget.
"It is simply a banjolele which ordinarily is worth maybe £400, but with the provenance, with who it belonged to, with that story, fascination... We pumped on a guide of between £20,000 and £30,000 and thankfully it came good."
George Harrison tried to buy the banjolele from Mr Wallin in the early 90s, but he would not part with it.
Decades later, Mr Wallin's family, from Sutton Coldfield, came across it during a clear out and decided to let it go.
Mr Wallin's son Terry, said: "He told me about George Harrison wanting to buy it but dad also bought an inscribed silver salver with the banjolele which was given to George Formby and his wife Beryl by theatre impresario Tom Arnold.
"George Harrison didn't want the silver salver, just the banjo ukulele, but dad wanted to keep everything together. That's why he wouldn't part with it."
There are only three of the Gibson banjo ukuleles which Formby used, and one was sold for £72,000 at auction to Queen's Brian May in 2008.
Who was George Formby?
George Formby Society
A banjo ukulele formerly owned by popular 1930s and 40s entertainer George Formby has been sold at auction for £28,500.