John Lennon, Paul McCartney, George Harrison and Ringo Starr's predecessor, drummer Pete Best, started playing backup for Sheridan in 1960 in Hamburg. The band made its first studio recordings with Sheridan the following year under the name The Beat Brothers, the Los Angeles Times said.
Among the songs they recorded were the Scottish folk track, "My Bonnie," with Sheridan singing lead; "Ain't She Sweet," which Lennon sang; and "Cry for a Shadow," an instrumental credited to Lennon and Harrison, the Times said.
Billboard.com said Sheridan continued performing in Hamburg while Lennon, McCartney, Harrison and Starr headed back to England, where the Beatles became wildly popular in 1963.
"Tony was a good guy who we knew and worked with from the early days in Hamburg," McCartney said in a statement to the Times Monday. "We regularly watched his late-night performances and admired his style. He will be missed."
The Times said Sheridan took part in a Beatles fan convention in San Diego last year, and then returned to Germany where he recently underwent heart surgery.
He died Saturday, but the cause of his death has not been disclosed.