The Sheffield born singer-songwriter 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 is reported to have been battling lung cancer, was “simply unique”.
Sir Paul McCartney said he was a lovely guy who “brought so much to the world”.
Known for his gritty voice, Cocker began his singing career in the pubs and clubs of Sheffield in the 1960s before hitting the big time.
He was propelled to pop stardom when his version of The Beatles’ 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.
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.
He was made an OBE in 2007. . .