The architect died in his sleep at a London hospital after a long illness and his loss has hit his famous clients hard.
A statement from the Stones reads: "The remarkable sets he designed for us over last two decades played a major part in the success of all those tours. His passion, dedication and professionalism was infectious. We all loved his dry sense of humour and unflappable demeanour.
"Mark will be sorely missed - not only by us but by every single member of ours and any crew he worked with."
Fisher recently helped to create a giant head of Williams for his current Take the Crown tour and the former Take That star marked his tragic death during a concert in Glasgow, Scotland on Tuesday night by dedicating his hit song Angels to his pal.
Taking to Twitter.com, the singer added, "R.I.P Mark Fisher, music's greatest architect. He will be missed."
Fisher, who was awarded an Order of the British Empire in 2000, was also known for his work with Pink Floyd and was the brains behind U2's massive 360-degree 'claw' stage.
He was also involved in stage designs for Queen musical We Will Rock You and both the opening and closing ceremonies for the London Olympics last year (12) and the 2008 Games in Beijing, China.