The singer had colon and liver cancer and, despite brief improvements in his health in recent months, passed away on Sunday evening.
Gibb died at the London Clinic surrounded by his second wife Dwina, sons Spencer and Robin-John and daughter Melissa.
Barry, now the last surviving member of the Bee Gees, had been in Britain in recent weeks to see his ailing brother, but was in the United States when he died.
Funeral arrangements are expected to be announced later this week, a spokesman said.
"The family have asked that their privacy is respected at this very difficult time," read a statement on Gibb's website.
Fans, fellow musicians and politicians paid tribute to the musician, and at the Billboard Music Awards in Las Vegas late on Sunday the show stopped for a moment of silence to honor him.
Actor John Travolta, who played the white-suited dance king Tony Manero in "Saturday Night Fever," which featured music by the Bee Gees, paid tribute to Gibb.
"I thought Robin was one of the most wonderful people- gifted, generous, and a real friend to everyone he knew. And we'll miss him," Travolta said in a statement.
Canadian rocker Bryan Adams was among the stars who took to Twitter to say farewell.
"Robin Gibb RIP. Very sad to hear about yet another great singer dying too young," he wrote, referring to the death on Thursday of another giant of the disco era, Donna Summer. She was 63.
In Britain, former Prime Minister Tony Blair, a friend, called Gibb "a highly intelligent, interested and committed human being.
"He was a great friend with a wonderful open and fertile mind and a student of history and politics. I will miss him very much," he said in a statement. "My thoughts and prayers are with Dwina and all the family."
Gibb spent much of a career spanning six decades pursuing solo projects. But it was his part in one of pop's most successful brother acts, the Bee Gees, that earned him fame and fortune.
Born in 1949 on the Isle of Man, located between England and Ireland, Robin and his family moved to Manchester where the brothers performed in local cinemas.
They went to live in Australia where the Bee Gees as a group was officially born, and in 1963 released the first single "The Battle Of The Blue And The Grey."
Believing their future lay in Europe, the Gibb brothers travelled to England to pursue a career in music and had their first British number one with "Massachusetts" in 1967.
TRAIN CRASH
The same year, Robin and wife-to-be Molly survived the Hither Green rail crash in south London that claimed around 50 lives. He later recalled that they probably would have been killed had they not been sitting in a first class carriage.
Rather than build on the early successes, the Bee Gees almost threw away the promising career they had worked so hard to achieve.
After recording the double-LP set "Odessa," the siblings fell out over which track should be the single and Robin walked out. Two years later the Gibbs were back together, and the 1970s was to belong to them.
Early in the decade they released the ballads "Lonely Days" and "How Can You Mend a Broken Heart," which topped the U.S. charts in 1971.
They struggled to maintain the momentum and critics felt the brothers had become stale until, in 1975, the Bee Gees changed course with an emphasis on dance-friendly tunes featuring high harmonies on their 13th album "Main Course."
It produced the catchy chart-topper "Jive Talkin'," which then led to an invitation to contribute to the soundtrack for the upcoming movie "Saturday Night Fever."
The Bee Gees' contributions would prove the pinnacle of their fame - "Stayin' Alive," "How Deep Is Your Love," "Night Fever" and "More Than a Woman" are all among their most recognizable songs, featuring the band's distinctive high vocals and harmonies, disco beats and slower romantic ballads.
LONG BATTLE WITH ILLNESS
The Bee Gees achieved superstardom with album sales estimated today at up to 200 million, putting them in the same league as the likes of the Rolling Stones and Pink Floyd.
Explaining their success, Bruce Elder of the All Music Guide wrote: "The group ... managed to meld every influence they'd ever embraced, from the Mills Brothers and the Beatles and early-'70s soul, into something of their own that was virtually irresistible."
The magic did not last, however, and with the disco era waning Robin and his brothers faded quickly into obscurity, concentrating in the 1980s on producing and writing for other acts including Diana Ross.
A 1987 comeback album "E.S.P." was moderately successful and included the hit "You Win Again," although in the 1980s Robin was actively pursuing his solo career.
In 1988 Andy Gibb, the youngest brother who was also a pop star and teen idol, died aged 30. Maurice passed away in January 2003, at 53, of complications from a twisted intestine, a condition that plagued Robin towards the end of his life.
According to online reports, in 2010, Robin had surgery for a blocked intestine and suffered further stomach pains last year forcing him to cancel a series of shows in Brazil.
During surgery a tumor was discovered and he was diagnosed with cancer of the colon and, subsequently, the liver. In February he spoke of a "spectacular" recovery and later that month performed on stage for the last time in a charity concert in London.
But he fell ill again and was unable to attend the world premiere of "The Titanic Requiem," his first classical work written with son Robin-John.
Robin-John told Reuters at the event that his father had contributed much of the requiem to the famous shipping disaster while in hospital.
(Reporting by Mike Collett-White, Piya Sinha-Roy, Bob Tourtellotte, Stephen Addison and Li-mei Hoang; writing by Mike Collett-White; editing by Paul Casciato)
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