The announcement was made by his family with “great sadness.”
The British-born Gibb’s musical career began when he formed the Bee Gees with his brothers Barry and Maurice in 1958.
The group is among the biggest-selling of all time with hits spanning five decades, including Stayin’ Alive, How Deep Is Your Love, Massachusetts and Night Fever.
Gibb’s family said in a statement: “The family of Robin Gibb, of the Bee Gees, announce with great sadness that Robin passed away today following his long battle with cancer and intestinal surgery.
“The family have asked that their privacy is respected at this very difficult time.”
Broadcaster Paul Gambaccini described the singer as “one of the major figures in the history of British music.”
The singer Dionne Warwick, whose biggest hit Heartbreaker was written by the Gibb brothers, said of Robin: “He was wonderful. He was a jokester. He had an incredibly witty sense of humor and was fun to be around. All three of them were sensational gentlemen first, just fun loving guys.”
The Gibb brothers were born in the Isle of Man but grew up in Manchester, later moving to Australia.
The Bee Gees notched up album sales of more than 200 million worldwide since their first hits in the 1960s.
“Everyone should be aware that the Bee Gees are second only to Lennon and McCartney as the most successful songwriting unit in British popular music,” Gambaccini said.
Robin Gibb had “one of the best white soul voices ever,” he said, adding that the group’s accomplishments had been “monumental.”
“Not only have they written their own number one hits, but they wrote huge hit records for Barbra Streisand, Diana Ross, Dionne Warwick, Celine Dion, Destiny’s Child… the list goes on and on.”
Former UK prime minister Tony Blair, a friend of Gibb, has paid tribute, saying he would “miss him very much.”
“Robin was not only an exceptional and extraordinary musician and songwriter, he was a highly intelligent, interested and committed human being,” Blair said.
Musicians have been taking to Twitter to pay their respects.
Canadian singer Bryan Adams wrote: “Robin Gibb RIP. Very sad to hear about yet another great singer dying too young.”
Fleetwood Mac’s Stevie Nicks wrote: “The soundtrack of my wonder years is vaporizing one artist at a time with these iconic musical losses lately.”
Justin Timberlake, meanwhile, described Gibb as “a truly brilliant musician,” adding: “One of my idols. My heart goes out to the Gibb family in this time of sorrow.”
Former BBC Radio 1 DJ Mike Read, who was a family friend, said: “Robin had the voice, the pathos, and he was a great writer.
“He had a gift for melody and a gift for lyrics and left a phenomenal legacy, a phenomenal catalogue.”
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