Mr. Cocker, a native of Sheffield, had been a journeyman singer in Britain for much of the 1960s, building a reputation as a soulful barreler with full-throated versions of Ray Charles and Chuck Berry songs. But he became a sensation after his performance of "With a Little Help From My Friends" at the Woodstock festival in 1969.
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His appearance there, captured in the 1970 concert film "Woodstock," established him as one of pop's most powerful and irrepressible vocalists. With his tie-dyed shirt and shaggy muttonchops soaked in sweat, Mr. Cocker, then 25, pleadingly teased out the song's verses—"What would you do if I sang out of tune?/Would you stand up and walk out on me?"—and threw himself into repeated climaxes, lunging and gesticulating in ways that seemed to imitate a guitarist on a heroic solo.
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On Twitter, Ringo Starr wrote on Monday, "Goodbye and God bless to Joe Cocker from one of his friends." And in a statement, Paul McCartney recalled hearing the recorded version of Mr. Cocker's cover, saying, "It was just mind-blowing, totally turned the song into a soul anthem, and I was forever grateful for him for having done that."
After Woodstock, Mr. Cocker toured widely and took his place as perhaps the rock world's most distinctive interpreter of other musicians' songs—an art then going out of fashion with the rise of folk-inspired singer-songwriters and groups, like the Beatles, that wrote their own material.
His other hits included a version of the Box Tops' hit "The Letter" and the standard "Cry Me a River" in 1970, and "You Are So Beautiful" in 1975. His only No. 1 was "Up Where We Belong," recorded as a duet with Jennifer Warnes for the 1982 film "An Officer and a Gentleman." Mr. Cocker won his lone Grammy Award for the performance.
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He released 22 studio albums, most recently "Fire It Up," in 2012.
At a concert earlier this year, Billy Joel called Mr. Cocker "a great singer who is not very well right now." Mr. Joel added, "I think he should be in the Rock and Roll Hall of Fame. I'm amazed that he's not yet, but I'm throwing in my vote for Joe Cocker."