BBC reported Monday that Barrie Marshall confirmed Cocker's death.
The Sheffield-born musician died after a "hard-fought battle with small cell lung cancer," said his record label, Sony.
Known for his gravelly voice and charismatic stage performances, Cocker shot to fame in the 1960s when his version of With a Little Help From My Friends made it to No. 1 on the charts. The song was released by the Beatles in 1967 on their critically acclaimed Sgt. Pepper's Lonely Hearts Club Band studio album.
Cocker's 1969 performance of the song at Woodstock has become one of the most iconic moments to come out of the legendary American rock music festival. Cocker's nostalgic version was also used as the theme song to the hit television series The Wonder Years in the 1980s and 1990s.
The ballad You Are So Beautiful, with Cocker's voice cracking on the final emotional note, was a Top 10 hit in 1975. He reached the top of the charts in the 1980s with the duet Up Where We Belong, with American singer-songwriter Jennifer Warnes.
The platinum-certified, Grammy Award-winning track also appeared in the 1982 movie An Officer and a Gentlemen, starring Richard Gere and Debra Winger.
Cocker also had hits with Randy Newman's song, You Can Leave Your Hat On and When the Night Comes.
He recorded 40 albums in his four-decade career and influenced the work of many other artists.
Canadian rocker Bryan Adams turned to Twitter to express his grief over losing his "good friend."
"You were one of the best rock singers EVER," wrote Adams.
Last year, Cocker and his band toured Europe for two months on the heels of his new album, Fire It Up.