Gibb, who sold more than 200 million records and notched up dozens of hits with brothers Maurice and Barry, had recently undergone intestinal surgery.
His family announced his tragic death with "great sadness" yesterday prompting an outpouring of emotion from fans and fellow members of the music industry.
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".
Stars including rock star Bryan Adams and singer songwriter Mick Hucknall also paid emotional tributes.
A statement released by Gibb's loved-ones said: "The family of Robin Gibb, of the Bee Gees, announce with great sadness that Robin passed away following his long battle with cancer and intestinal surgery. The family have asked that their privacy is respected at this very difficult time."
The Bee Gees' song catalogue, which includes Massachusetts, I've Gotta Get A Message To You, Lonely Days, How Can You Mend A Broken Heart, 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 number one 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.
"What must also be said is Robin had one of the best white soul voices ever. He was singing lead on his first number one when he was 17, that was Massachusetts."
Gibb had surgery on his bowel 18 months ago for an unrelated condition but a tumour was discovered and he was diagnosed with cancer of the colon and subsequently of the liver.
The singer fell into a coma last month after contracting pneumonia but his family later said he had "beaten the odds" just days after doctors said he "was in God's hands" and had a 10% chance of survival.
His twin brother Maurice died of a heart attack in 2003 following intestinal surgery, while his younger brother Andy, who was not part of the Bee Gees but a successful singer in his own right, died in 1988 from heart failure at 30.
Many people took to micro blogging site Twitter to pay their respects.
A statement posted by Sony Music said: "Rest in peace, Robin Gibb. Thanks for the music."
Former deputy prime minister John Prescott wrote: "Just heard about Robin Gibb.
"A good friend, a brilliant musician and a man who turned all of us into wannabe Travoltas!
"Rest in peace Robin."
Canadian rocker Adams was also among the stars paying tribute, saying: "Robin Gibb RIP. Very sad to hear about yet another great singer dying too young."
While British singer songwriter Mick Hucknall wrote: "RIP Robin Gibb. A musical giant," while former X Factor judge Dannii Minogue said: "We start believin' now that we can be who we are - Grease is the word...RIP Robin Gibb."
Eighties rock band Duran Duran also posted on their feed: "Sorry to hear about the passing of Robin Gibb of the BeeGees. Our condolences to his friends and family."
Radio disc jockey Mike Read, who was a family friend of Gibb, said the singer had an "incredible voice".
"Robin had the voice, the pathos, and he was a great writer," he added in remarks to BBC Radio 5 Live.
"He had a gift for melody and a gift for lyrics and left a phenomenal legacy, a phenomenal catalogue."
Referring to the Bee Gees, the former BBC Radio One DJ said: "They had every accolade under the sun. They were able to write great commercial songs that touched people over a very long period of time. They had every award, every gold disc, every platinum disc, the Grammys the lot and had been doing it so long but were still so good at it."
Gambaccini described Gibb as one of the most influential British artists ever.
"He was one of the important figures in the history of British music - and I mean of all time, I don't mean just the last few years or the rock era, I mean of all time," he told BBC Radio 5 Live.
"He and Barry and Maurice wrote 23 number one records (with the exception of Maurice who wrote 22). They are the only song writers to have number ones in the last five decades. They did briefly have the number one album of all time - Saturday Night Fever. Something of this magnitude is bigger than just the last few years."
Gibb had been due to premiere a collaborative classical work, The Titanic Requiem, with his 29-year-old son Robin-John in April, but the event went ahead without him due to his poor health.
The long-standing Labour supporter raised eyebrows in 2008 when he suggested then prime minister Gordon Brown let his hair down after a hard day running the country by turning on the stereo and blasting out Bee Gees disco classics.
"He listens to our music every day. Gordon likes our music and I like Gordon," he told The Times.
He appeared on party platforms during the 2005 election and even invited Tony Blair to stay at his Miami home. The pop star said that he got on with the former leader "like a house on fire".
Former prime minister Tony Blair, a friend of Gibb, added his tribute today, 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," he said.
"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 Dwina and all the family."
OBITUARY
Robin Gibb - alongside his brothers in the Bee Gees - provided decades of chart hits and helped to turn disco into a worldwide phenomenon with tracks such as Night Fever and Stayin' Alive.
With his twin brother Maurice, who died in 2003, and elder brother Barry, Gibb notched up dozens of hits - as performers and writers - and sold more than 200 million records.
The Bee Gees' song catalogue, which includes Massachusetts, I've Gotta Get A Message To You, Lonely Days, How Can You Mend A Broken Heart, 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.
But it will be the group's contribution to the late 70s disco boom - and in particular the Saturday Night Fever soundtrack - which will long be seen as his and the group's most enduring legacy.
Posing with toothy smiles, bouffant hair and tight white outfits on the album's cover, they captured the look of an era. And with their falsetto close harmonies hitched to a new dancefloor-friendly sound, the trio's career was propelled to new heights.
They sang on fewer than half the songs on the soundtrack to the 1977 film, which brought John Travolta to the attention of the film world for his portrayal of a working class boy who lived to strut his stuff.
But as one of the biggest selling albums of all time, it brought recognition for their new direction (two of the songs had featured on earlier albums) and paved the way for the even bigger Spirits Having Flown in 1979.
Spirits, which went on to sell 30 million copies, included songs such as Tragedy and became the group's first and only UK number one studio album. It was also their first appearance in the UK albums top 40 for a decade.
The new-found reputation of the Bee Gees was far removed from their beginnings as a young trio performing in theatres in Manchester in the mid-1950s.
Robin and his twin Maurice were born on the Isle of Man to English parents on December 22, 1949, three years after their brother Barry.
The trio started out as a child act encouraged by their father Hugh, a band leader, and their mother Barbara, a former singer. They continued performing when the family moved to Brisbane, Australia, in 1958.
They took the name Bee Gees, an abbreviation of Brothers Gibb, signed to the Australian label Festival Records and released a series of singles written by Barry while in their teenage years.
The group were popular and released an album but they failed to top the charts Down Under until they had headed back to the northern hemisphere to try to find success.
Their single Spicks And Specks went to number one in Australia while they were signing a record contract in the UK and their first recording under that deal - New York Mining Disaster 1941, released in mid-1967 - made the top 20 on both sides of the Atlantic.
But the group's first major hit was the chart-topping single Massachusetts, showcasing their ability as arrangers. The brothers soon followed the lead set by The Beatles and Rolling Stones as they embraced experimentation, tackling different styles.
They recorded the album Idea and from it released I Started A Joke and Gotta Get A Message To You, both hits. But the brothers argued over the follow-up album Odessa, released in 1969, and did not record together for 18 months.
Regrouping in 1970, they created their first US number one Lonely Days, and the following year had another hit with How Can You Mend A Broken Heart, covered by soul legend Al Green.
But as tastes and the musical landscape changed, their star slipped and they lost ground.
It was teaming up with producer Arif Mardin - who had worked with Aretha Franklin, Dusty Springfield and many other soul legends - which sowed the seeds for the change in sound.
Jive Talkin' featured on their second Mardin-produced release, the Main Course album, and they went on to continue with the dance groove on follow-up Children Of The World.
It was the group's manager Robert Stigwood who brought them on board for Saturday Night Fever, a film he was producing, and the songs were written in little over a weekend. Disco was already established but the music and the film combined to give it even greater popularity.
But tastes changed once again and as the disco boom ended, so their sales took a hit and the trio became virtually invisible for a few years, concentrating on solo material and producing hits for other artists.
But they staged a comeback in 1987 - almost grand statesmen of pop, despite Robin and Maurice only being in their late 30s - with a new album and a return to the top of the singles charts with You Win Again.
Songwriting for others also yielded numerous chart hits including Dionne Warwick's Heartbreaker, Diana Ross's Chain Reaction and Islands In The Stream for Dolly Parton and Kenny Rogers.
"A lot of these songs in our catalogue are still on the radio," Robin said in an interview in 2011.
"I can turn the radio on, on any given commercial radio station including the BBC, and hear five Gibb brothers' songs a day - also in America - because of all the other artists we have written for, as well as ourselves."
The family suffered a setback when younger brother Andy - who had his own pop success - died in 1988 from heart failure at the age of 30.
And 15 years later there was further heartache for the family when Maurice died in Miami, due to a complication from a twisted bowel.
Robin found it particularly hard to come to terms with the 2003 death of his twin.
In an interview seven months later, he said: "He was part of the fabric of my life. We were kids together, and teenagers. We spent the whole of our lives with each other because of our music.
"I can't accept that he's dead. I just imagine he's alive somewhere else."
Robin was later to suffer from the same bowel condition which led to his brother's death, leading to his own protracted bout of ill health.
However in 2011 he finished recording his first solo album in seven years, a collection tentatively titled 50 St Catherine's Drive.
In the same year he re-recorded a Bee Gees song for Remembrance Day, the 1968 hit I've Gotta Get A Message To You, with military group The Soldiers in aid of the Poppy Appeal.
Gibb last performed on stage in February, supporting injured servicemen and women at the Coming Home charity concert held at the London Palladium. He had been due to premier his classical work The Titanic Requiem in April with son Robin-John, but the event went ahead without him due to his poor health.
When not touring or recording, he divided his time among his homes in Oxfordshire, Miami and the Isle of Man.
He had a great passion for history and was involved in a campaign to build a permanent memorial in London for the veterans of the Second World War's Bomber Command.
He was married twice, to Molly Hullis, a secretary in the organisation of impresario Robert Stigwood, from 1968 to 1980, then to Dwina Murphy-Gibb, an author and artist. He had two children, Spencer and Melissa, from his first marriage, and a son, Robin-John, from his second.
He was made a CBE in the 2002 New Year's Honours List, along with his brothers.
