Wright died at his home in England on Monday.
Wright, guitarist Roger Waters and drummer Nick Mason founded the band that became Pink Floyd in the 1960s when they were students.
Pink Floyd went on to become one of the biggest names in rock.
"The family of Richard Wright, founder member of Pink Floyd, announce with great sadness that Richard died today after a short struggle with cancer," his spokesman said in a statement.
"The family have asked that their privacy is respected at this difficult time."
Wright co-wrote five songs on the Dark Side Of The Moon LP which was released in 1973 and spent 14 years on the Billboard 200 album chart to become one of the best-selling albums ever.
Wright left Pink Floyd after falling out with Waters during sessions for The Wall.
He rejoined the band in 1987.