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.
McCartney 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 Starr.
The veteran drummer echoed McCartney's sentiments with a short Twitter message.
Starr wrote: "Just say goodbye to Tony Sheridan just he died. I had a great month 1960/61 playing with him was great."
Ringo Starr paid his respects to Tony Sheridan who passed away recently
Sheridan met the group in the 1960s in Germany and they recorded tracks such as 'My Bonnie' and 'The Saints' together, as The Beatles acted as Sheridan's back-up band on the Hamburg club scene.
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.
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