The Sheffield-born singer had a career lasting more than 40 years, with hits including You Are So Beautiful and Up Where We Belong.
His agent Barrie Marshall said Cocker, who died after battling lung cancer, was "simply unique".
Report informs citing BBC News, Sir 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."
Wakeman told BBC Radio 2: "The great thing is with someone like Joe is what they leave behind, and that will be with us for years and years."