Gibb, who sold over 200m records and notched up dozens of hits with brothers Maurice and Barry, had recently undergone intestinal surgery.
They began performing together when twins Robin and Maurice were just six and Barry was nine, singing cover versions of hit songs at their local cinema in Manchester.
His family announced his tragic death with “great sadness”, prompting an outpouring of emotion from fans and fellow members of the music industry.
Respected BBC broadcaster Paul Gambaccini said the performer and songwriter was “talented beyond even his own understanding” and dubbed him as “one of the important figures in the history of British music”.
Musicians including rock star Bryan Adams and singer-songwriter Mick Hucknall also paid emotional tributes.
The band’s song catalogue, which includes ‘Massachusetts’, ‘How Deep Is Your Love’, and ‘Stayin’ Alive’, led to their induction into both the Rock and Roll Hall of Fame and the Songwriters’ Hall of Fame.
Gambaccini said: “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.
“Their accomplishments have been monumental. Not only have they written their own No 1 hits, but they wrote huge hit records for Barbra Streisand, Diana Ross, Dionne Warwick, Celine Dion, Destiny’s Child, Dolly Parton and Kenny Rogers, the list goes on and on.”
Gibb was hailed as a master musician whose interests went far beyond the recording studio.
The distinctive singer, who also wrote and arranged numerous hits for other major artists, was also recognised for his work on behalf of British soldiers and his interests in politics, history and the Titanic.
Former British prime minister Tony Blair, a longtime friend of Gibb, said the singer had a “wonderful open and fertile mind” and offered condolences to Gibb’s widow, Dwina, and their family.
“Robin was not only an exceptional and extraordinary musician and songwriter, he was a highly intelligent, interested and committed human being,” he said.
Gibb suffered a lengthy illness and had appeared very gaunt in his rare public appearances during the past year. He was forced to cancel most of his engagements after he suffered alarming weight loss and required emergency intestinal surgery.
He did find the energy, however, to compose The Titanic Requiem with the help of his son, RJ. However, Gibb lapsed into a coma and was too sick to attend the gala premiere with the Royal Philharmonic Orchestra last month.
The classical composition about the loss of the Titanic marked a new direction for the multitalented Gibb.
Gibb was a history buff who had worked overtime in his last few years to help create a permanent memorial to the flyers and crew who served during the Second World War.
Casual listeners knew the Bee Gees best for the innovative disco sound they created with the Saturday Night Fever soundtrack, but music industry insiders viewed the brothers Gibb as extremely versatile music makers.
Songs they wrote for other artists include ‘Islands in the Stream’ by Dolly Parton and Kenny Rogers, ‘Heartbreaker’ by Dionne Warwick, and ‘Woman in Love’ by Barbra Streisand.
Former Beatles drummer Ringo Starr, whose band competed against the Bee Gees for top chart spots in the 1960s, praised Gibb’s musical legacy.
“The Bee Gees from our era were quite important, especially the harmonies,” said Starr.
“He had a great voice and they wrote great songs.”