The Sheffield-born singer had a career lasting more than 40 years, with hits including 'You Are So Beautiful' and 'Up Where We Belong', reported BBC online.
His agent Barrie Marshall said Cocker, who died after battling lung cancer, was "simply unique".
Paul McCartney said he was a lovely guy who "brought so much to the world".
Cocker's friend Rick Wakeman, keyboard player for the rock band Yes, called his rendition of 'With a Little Help From My Friends' "sensational" and said: "He had a voice that was just unique."
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He was propelled to pop stardom when his version of 'With A Little Help From My Friends' reached number one in 1968.
He performed the song at the famous Woodstock Festival in New York state a year later.
He was also well-known for his Mad Dogs and Englishmen Tour of 1970, which visited 48 cities across the US.
His duet with Jennifer Warnes, 'Up Where We Belong' - from 'An Officer And A Gentleman' - hit number one and went on to win both a Grammy and an Academy Award in 1983.
Last year, his arena tour across Europe saw him achieve a number one album in Germany and give what was to be his final concert in Hammersmith, London, in June.
Cocker, who recorded 23 studio albums and 40 albums, lived in Colorado, in the US.