Wright, who played the keyboard and wrote music for classic albums The Dark Side Of The Moon and Wish You Were Here, died aged 65 after a short battle with cancer.
Speaking shortly after his death was announced, Pink Floyd guitarist Dave Gilmour said his musical partner and friend was “gentle, unassuming and private”.
He added: “His soulful voice and playing were vital, magical components of our most recognised Pink Floyd sound.
“Like Rick, I don’t find it easy to express my feelings in words, but I loved him and will miss him enormously.
“I have never played with anyone quite like him.”
In the early days of Pink Floyd, Wright was seen as the group’s dominant musical force, composing masterpieces such as The Great Gig In The Sky, and Us And Them.
“Without Us And Them and The Great Gig In The Sky, what would The Dark Side Of The Moon have been?” Gilmour said.
“Without his quiet touch the album Wish You Were Here would not quite have worked.
“In my view all the greatest PF moments are the ones where he is in full flow.”
London-born Wright mastered the trombone, saxophone, guitar and piano in his teenage years, and had hoped to emulate Miles Davis and John Coltrane, before enrolling in architecture at the Regent Street Polytechnic.
There he met fellow band mates Roger Waters and Nick Mason, and they went on to form the Pink Floyd Sound in 1965.
Their first studio album, The Piper At The Gates Of Dawn was released in 1967.
After tensions with Waters, Wright left the band shortly after recording sessions for The Wall in 1979.
He released two solo albums including Broken China in 1996, but they never attracted the band’s level of critical acclaim.
Gilmour said that the musician had “lost his way for a while” during that time.
He officially returned to the band in 1987, playing the keyboards and adding vocals to the A Momentary Lapse Of Reason album.
“In the early 90s, with The Division Bell, his vitality, spark and humour returned to him,” Gilmour said.
Wright performed on every Pink Floyd tour and played with the surviving members of the band at Live 8 in 2005.
His performances during those times were “uplifting”, Gilmour said.
“It’s a mark of his modesty that those standing ovations came as a huge surprise to him, (though not to the rest of us),” he said