Williams was the owner of the Jacaranda club in Liverpool, which confirmed the news of his death on December 30, reported The Guardian.
"His legacy has allowed us to remain at the heart of the Liverpool music scene for almost 60 years, and his memory will live on through every band that plays our famous stage. Allan, you will be missed.
"All of our thoughts and wishes go to his family and his wife Beryl," a message on the club's Facebook page read.
The Beatles Story, an exhibition in Liverpool celebrating the band's success, praised Williams for his "significant role".
"We are deeply saddened to hear of the passing of Allan Williams. Our thoughts go out to his family at this sad time. Allan was a friend to many of us at the Beatles Story and his legacy will continue to be told for years to come," the exhibition's spokesperson Martin King said.
Williams parted ways with the band in 1961 following a disagreement over his fee.