His other major hits included You Are So Beautiful in 1975 and Up Where We Belong in 1983, a duet with Jennifer Warnes from the movie An Officer and A Gentleman which won a Grammy.
A long-time US resident, Cocker died at home in Colorado where he lived on his Mad Dog Ranch named after his classic 1970 live album Mad Dogs & Englishmen.
His label Sony Music released a statement confirming Cocker's death.
It said: 'John Robert Cocker, known to family, friends, his community and fans around the world as Joe Cocker, passed away on December 22, 2014 after a hard fought battle with small cell lung cancer."
Cocker was born in Sheffield and by 1961 was living a double life, working as a gas fitter by day and, inspired by Ray Charles, as a pub singer at night in a series of bands.
As his star rose in the US in the wake of Woodstock, Cocker became a heavy drinker and drug user.
His performances - including his first New Zealand show at Western Springs in 1972 - suffered due to his alcoholism up until the mid 70s.
Throughout his career Cocker maintained a steady studio output, recording some 40 albums and making his name as an interpreter of other people's songs.
For a brief period in the late 70s, he tried writing his own material but it was his definitive versions of Jimmy Webb's The Moon's A Harsh Mistress, Leon Russell's Delta Lady, numerous Beatles songs, Billy Preston's You Are So Beautiful, Jimmy Cliff's Many Rivers To Cross, the Box Tops' The Letter and a dozen others for which he became known.
"Because of my vocal style I don't try and reinvent them. Even if the arrangement isn't that far removed from the original I try to bend them around in a certain way that gives them a new approach," he told the Herald in 2005.
"I'm an R'n'B singer but I've always liked pop ballads. "At heart I'm just an R'n'B singer with soul tinges."
Cocker was a frequent visitor to New Zealand in recent years, last playing at Vector Arena in 2011.
Cocker was awarded an OBE in 2007 for services to music.
He is survived by his American wife Pam Baker whom he credited with pulling him out of his drug and drink spiral in the late 1970s..
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