Syd Barrett released two solo albums after leaving Pink Floyd
The guitarist was the band's first creative force and an influential songwriter, penning their early hits.
He joined Pink Floyd in 1965 but left three years later after one album. He went on to live as a recluse, with his mental deterioration blamed on drugs.
"He died very peacefully a couple of days ago," the band's spokeswoman said.
"There will be a private family funeral."
He was the first guy I'd heard to sing pop or rock with a British accent - his impact on my thinking was enormous
"Syd was the guiding light of the early band line-up and leaves a legacy which continues to inspire."
David Bowie described Barrett as a "major inspiration", saying: "I can't tell you how sad I feel.
"The few times I saw him perform in London at UFO and the Marquee clubs during the '60s will forever be etched in my mind.
"He was so charismatic and such a startlingly original songwriter. Also, along with Anthony Newley, he was the first guy I'd heard to sing pop or rock with a British accent.
Barrett (third from left) struggled with drugs and fame in the 1960s
Born Roger Barrett in Cambridge, he composed songs including See Emily Play and Arnold Layne, both from 1967.
He also wrote most of their album The Piper at the Gates of Dawn. But he struggled to cope with fame and drugs.
Dave Gilmour was brought in to the band in February 1968 and Barrett left that April, releasing two solo albums soon after.
The band's biggest-selling releases, Dark Side of the Moon and The Wall, emerged in the post-Barrett era, with the band selling an estimated 200 million albums worldwide.
Just as Pink Floyd were about to achieve global success, Barrett retreated from public life and returned to Cambridge.
Little was known about his whereabouts for 20 years until he was tracked down living with his mother.
Barrett became one of rock's most reclusive characters
Former Blur guitarist Graham Coxon released a statement saying: "Lost him again... for bang on 20 years Syd led me to better places."
"From my agape 17-year-old first listen to Bike to, just the other day, Jugband Blues.
"Languished in his noise... dreamt in his night... stared at his eyes for answers..."
Barrett's biographer Tim Willis said the guitarist's music left a lasting legacy.
"I don't think we would have the David Bowie we have today if it wasn't for Syd," he told BBC Radio Five Live.
"Bowie was very much a kind of clone of Syd in the early years. His influence is still going.
"New bands discover him all the time. There's always a Syd revival going on - if it wasn't the punks, it was REM, and I'm sure that Arnold Layne and Emily Play as pop songs will live forever."