Cocker's performing career spanned some 50 years, from Woodstock, where he sang the Beatles' "With a Little Help From My Friends," to the digital-music era. He had tour dates scheduled well into 2015.
"Goodbye and God bless to Joe Cocker from one of his friends peace and love," tweeted Beatles drummer Ringo Starr.
Cocker began as a singer in England at the same time as the Beatles, with whom he was often linked. He played pubs across the country in a series of rock bands before he and his Grease Band recorded "With a Little Help From My Friends" in 1968 with Jimmy Page, Steve Winwood and others.
The song became a No. 1 hit in England and propelled him to Woodstock, where his passionate live version was a festival highlight and launched his U.S. career.
Cocker scored another major success in the early 1970s with "Mad Dogs and Englishmen," a live album and concert film.
"Up Where We Belong," his duet with Jennifer Warnes from the movie "An Officer and a Gentleman," was Cocker's biggest U.S. hit, topping the Billboard singles charts in 1982. It also won him a Grammy, and the Oscar for best original song.
Cocker was known for his spasmodic movements on stage, where he often flailed his arms as he sang. His distinctive moves, he said, were almost accidental.
"I never played organ or piano or guitar, so it was more out of frustration and me just trying to impersonate in a way," Cocker told the Broward-Palm Beach New Times in 2012. "I did it subconsciously. People mistook for me being ill, like I had palsy. I'm not nearly so demonstrative now, but I still have my own way of feeling the rhythm."
Cocker also had lesser hits with covers of torch classic "Cry Me a River," Traffic's "Feeling Alright," the Boxtops' "The Letter" and the Beatles' "She Came in Through the Bathroom Window."
In the 1980s his witty cover of Randy Newman's "You Can Leave Your Hat On," was featured in the erotic drama "9 1/2 Weeks" and became a strip-tease anthem.
The singer told the Daily Mail in 2013 that by the 1970s his descent into drugs and alcohol had become so severe that he sometimes forgot the lyrics to songs.
"If I'd been stronger mentally, I could have turned away from temptation," Cocker said. "But there was no rehab back in those days. Drugs were readily available, and I dived in head first. And once you get into that downward spiral, it's hard to pull out of it. It took me years to get straight."
He credited his wife, Pam, with helping him get sober.
"It was Pam who helped me get myself back together," he said. "She made me think positively. I was very down on myself. She made me realize people still wanted to hear me sing, and convinced me I could escape the downward spiral."
In 2012 he released the album, "Hard Knocks." That year he talked to NPR about the project and his love of his life in Colorado -- despite the harsh winters.
"I embrace the winter these days," he said in the interview. "The best thing to do is get a big house. If you are going to have cabin fever, have a big cabin. I walk on a regular basis, I have a couple of dogs. The house tucks right into the mountains. I literally feel I have become a mountain man over these past couple of years."
Musicians of all ages and genres took to Twitter to pay tribute.
"So sad to hear about Joe Cocker. What an entertainer. One of a kind voice. Rock won't ever sound the same," tweeted "Glee's" Kevin McHale.