"God bless George Martin peace and love to Judy and his family," Starr tweeted.
Starr followed the message by posting a photo of the Fab Four with Martin, saying "Thank you for all your love and kindness George."
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A Universal Music Group spokesman in Los Angeles confirmed Martin's death but said details were not immediately known.
Martin was referred to as the "fifth Beatle" and served as producer, collaborator and mentor to John Lennon, Paul McCartney, George Harrison and Ringo Starr.
During his six-decade career in the music industry, Martin produced almost all of the Beatles' recordings and also worked with Gerry & the Pacemakers, Jeff Beck, America, Cheap Trick and other acts.
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He produced jazz, comedy and classical albums before signing the Beatles in 1962. The young band members were rough around the edges, but Martin saw their commercial promise.
Over the coming years, he helped score, arrange, and produce many of the band's biggest hits, including "Yesterday" and "Love Me Do." His 1979 autobiography, "All You Need Is Ears," chronicles his discovery of the Beatles and their creative process.
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Martin was knighted in 1996. In 2006, working with his son, Giles Martin, he helped develop the Beatles-inspired Cirque du Soleil show "Love" in Las Vegas, which went on to reap his two most recent Grammys.
Martin was named by Guinness World Records as the most successful producer ever, with more than 50 No. 1 hit records over five decades in the United States and Great Britain alone.
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