Sheridan sang on some of the Fab Four's earliest records and was even the star of the Beatles' first commercial recording in which they performed as his backing band.
Paul posted a message on his website which read: "Tony was a good guy who we knew and worked with from the early days in Hamburg.
"We regularly watched his late night performances and admired his style. He will be missed.”
The one-time Beatles frontman passed away in Hamburg, Germany at the age of 72 after a long illness and has been labelled as a "good guy" by old friend Ringo.
Ringo echoed Paul's sentiments with a short Twitter message.
Ringo wrote: "Just say goodbye to Tony Sheridan just he died. I had a great month 1960/61 playing with him was great."
Ringo paid his respects to Tony Sheridan who passed away recently
They went on to perform together at times and Sheridan even claimed that he was responsible for arranging Ringo's first performances with the Beatles.