STAR VISIT: Robin Gibb arrives at Paisley Museum during the filming of Who Do You Think You Are? in 2011. Picture: James Galloway
The songwriter had been ill for many months with a serious bowel condition, and had battled pneumonia in addition to colon cancer.
Household names from the world of pop and politics paid tribute to Gibb.
Former prime minister Tony Blair said: "Robin was not only an exceptional and extraordinary musician and songwriter, he was 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. My thoughts and prayers are with [Gibb's widow] Dwina and all the family."
Gibb appeared on Labour Party platforms during the 2005 election and invited Blair to stay at his Miami home. The singer said he got on with Blair "like a house on fire".
Blair's former deputy PM, John Prescott, wrote: "A good friend, a brilliant musician and a man who turned all of us into wannabe Travoltas," referring to the Saturday Night Fever soundtrack LP, to which the Bee Gees contributed.
Broadcaster Paul Gambaccini described Gibb as "one of the important figures in the history of British music", adding: "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."
"Top guy, wonderful singer, and one of Britain's greatest ever musical success stories," wrote US TV chat-show host Piers Morgan, while Take That singer Gary Barlow tweeted: "Such a great loss. His music will outlive us all."
Canadian rocker Bryan Adams said: "Very sad to hear about yet another great singer dying too young." Jake Shears, of the bestselling act, The Scissor Sisters, tweeted: "You are and forever will be a massive influence and inspiration."
Cycling legend Lance Armstrong said he continued to be "saddened" to see cancer taking "our loved ones".
Armstrong, a seven-time Tour de France winner, who has had his own, highly-publicised struggle with cancer, added in a post to his 3.45 million Twitter followers: "Gotta put a stop to it."
Last year the BBC programme Who Do You Think You Are? showed Gibb in Paisley as he researched his family's past. His great-grandfather, Matthew Gibb, who grew up in poverty in the town, went on to become a decorated sergeant in the Indian Army. Gibb also met a cousin, Ann, Matthew's last surviving granddaughter.