Shades of John Lennon, or a Professor
Lennon gave the hat – along with a toy gun – to his uncle Charlie Lennon, who was a great fan of western films. Uncle Charlie passed them on to Larry Warren, an American who lives in the Beatles' home city of Liverpool.
Warren said: "I knew Charlie Lennon well and I bought these items from him. He didn't want to take any money for them but I insisted.
"I have helped conserve other items concerned with the Beatles, including parts of the church hall where Lennon first met Paul McCartney.
"The cowboy hat was something that Lennon had on the US tour in 1965 – I think they all had one. He gave it to his uncle in about 1967 along with a toy six-shooter gun because his uncle loved western films. But the hat was too big for his uncle and that amused Lennon."
Also up for sale is a pair of black Italian sunglasses owned by Lennon in 1967 that may go for up to £4,000.
Lennon passed the sunglasses to his uncle when Charlie visited the singer's mansion in Weybridge, Surrey, on a sunny day.
Warren said: "He gave the sunglasses to his uncle at his home in Surrey in about 1967. He had a swimming pool there and they'd been out in the sun.
"Charlie authenticated both items and I've had them for 10 years. Charlie died some years ago so it is time to move them on."
Beatles memorabilia, especially items connected with Lennon, who was shot dead in New York in 1980 aged 40, are hugely popular with collectors and Beatles fans.
Glen Norcliffe, of the Berkshire-based auctioneers Cameo, said: "These are wonderful items that belonged to John Lennon when he was at the height of his career.