Wright played the keyboard with the legendary band and wrote music in classic albums like the Dark Side Of The Moon and Wish You Were Here.
His spokesman said: "The family of Richard Wright, founder member of Pink Floyd, announce with great sadness, that Richard died today after a short struggle with cancer.
"The family have asked that their privacy is respected at this difficult time."
Wright's fellow band member, David Gilmour, led the tributes. “I really don’t know what to say other than that he was such a lovely, gentle, genuine man and will be missed terribly by so many who loved him. And that’s a lot of people,” Gilmour said.
The self-taught keyboardist and pianist met band members Roger Waters and Nick Mason while at architecture school.
He was a founder member of The Pink Floyd Sound in 1965, and the group's previous incarnations, such as Sigma 6.
In the early days of Pink Floyd, Wright, along with Syd Barrett, was seen as the group's dominant musical force.
The London-born musician and son of a biochemist wrote and sang several songs of his own.
The Great Gig In The Sky, and Us And Them, both from 1973's seminal Dark Side Of The Moon album, were his most well-known compositions.
He also made essential contributions to Atom Heart Mother, Echoes and Shine On You Crazy Diamond, the tribute to former band member Barrett.
Wright recorded his first solo project, Wet Dream, in 1978.
After his relationship with Waters became increasingly difficult, he left Floyd following sessions for the album The Wall.
Wright was retained as a salaried session musician during live concerts in 1980 and 1981.
In 1983, Pink Floyd released the only album in which Wright does not appear - The Final Cut.