The school (GSA) has announced £750,000 of donations towards the appeal for funds to rebuild Charles Rennie Mackintosh's architectural masterpiece, which was devastated by fire in May.
The GSA has also received donations from the Hugh Fraser Foundation and £150,000 in individual donations.
The Hugh Fraser Foundation, long-term supporters of the GSA, has pledged £300,000.
Sir Cameron, the producer of shows such as Les Miserables, The Phantom of the Opera, and Cats, said: "Since I became a theatre producer I have taken great pleasure from having a namesake as illustrious as Charles Rennie Mackintosh.
"His legacy as an artist and designer, and his unique style and invention, lived on through the amazing building he designed for the Glasgow School of Art.
"Successive generations of artists have been inspired and nurtured within its walls.
"It is hardly surprising the tragic news of the fire spread globally and we are all encouraged by the GSA's clear determination to restore the wonderful building.
"My admiration for C R Mackintosh and my personal passion for original architectural design makes me even more pleased to be able to become one of the first donors."
Dr Kenneth Chrystie, chairman of the Hugh Fraser Foundation, said: "The Trustees of the Hugh Fraser Foundation were clear that we wished to make a major and public show of support for the School following the fire.
"We felt that it was a great privilege to be able to support the GSA to begin the process of reconstruction and recovery.
"I am confident that the fundraising appeal will attract world-wide support from those who share with us the desire to see the school not only recover, but regain momentum towards its future success".
Professor Tom Inns, director of the GSA, said: "We have been moved by the incredible generosity that we have experienced since the fire. We are hugely grateful to both the Hugh Fraser Foundation and the Cameron Mackintosh Foundation for their early commitment to the Mackintosh Appeal and their significant support.
"The GSA has been honoured to have the financial and personal support of the Hugh Fraser Foundation over many years, and this most recent donation is very much appreciated.
"The kind words of Sir Cameron and the support of The Mackintosh Foundation are also most welcome at this difficult time."
He continued: "I would also like to extend the heartfelt thanks of the Glasgow School of Art to all the institutions and individuals who have donated to the Appeal to date.
"This support, along with the many, many messages of good will and offers of academic and other expert support, has meant so much to us."
The Mackintosh Appeal, launched by the Glasgow School of Art Development Trust on 18 June has trustees including Peter Capaldi, Bryan Ferry and the leading Hollywood actor Brad Pitt.
The appeal hopes to raise a total of £20m.
The Scottish Government has said it will provide up to £5m in matched funding to support the GSA in its recovery.
The UK Government also recently said it would give £5m to The Mackintosh Appeal.