A front page photo shows Paul McCartney crowning the carnival queen in Northwich, Cheshire, in 1963.
It was taken by photographer Les Goode and featured in Alkali News - an in-house magazine for chemical company ICI.
He sent it off to the Beatles to be autographed, but John Lennon signed it on behalf of all four band members.
'Full of mischief'
He wrote: "All the best from the Beatles" before sending it back to Mr Goode.
Liverpool auctioneers Adam Partridge said Cheshire photographer Mr Goode had worked with the Beatles before and had known them for a while.
A spokesman said: "Mr Goode's widow said Lennon was a big character who was full of mischief so she was sure her husband knew the signatures were all in the hand of John Lennon.
"In fact that's the reason it sold today."