The cash boost will help repair the destruction caused by a massive blaze which ripped through the Charles Rennie Mackintosh masterpiece.
Chief Treasury Secretary Danny Alexander said the money will go towards a £20m Art School appeal, launched after last month's blaze.
Details of the UK government's financial support, come on top of a pledge of up to £5m from the Scottish Government to help restore the building.
Mr Alexander, said today: "The Glasgow School of Art is one of Glasgow's great institutions.
"The response to the fire from people across the world has been phenomenal.
"I am delighted to be able to announce that the UK government will be providing £5m to the Mackintosh Appeal to help the GSA recover and then continue to thrive.
"It is a beautiful building of international importance so it is right that the UK government should make a contribution to its restoration.
"We will work with The Glasgow School of Art to ensure that the funding is provided at the most appropriate time to meet their needs."
The appeal cash will be used to help rebuild the fire-ravaged Mackintosh Building.
Firefighters managed to save 90% of the world famous building and 70% of the contents but it is estimated it could cost up to £35m to restore.
Art School director Professor Tom Inns said: "The UK Government's funding announcement is a huge boost to the GSA Development Trust's Mackintosh Appeal.
"We are determined to restore the building to its former glory, as the inspirational home for the GSA's creative talent and for the delight of visitors.
"The UK government's support will help us enormously in our efforts to rebuild.
"And to ensure we can continue to operate at the highest level internationally, allowing the world to understand the unique contribution of Mackintosh."
The city and the arts world were rocked on May 23 when flames engulfed the A-listed building.
Students were putting the final touches to their end-of-year projects at the time.
The library was destroyed, but the Mackintosh Museum and the archives survived.
Hollywood star Brad Pitt and Scots actor and former Art School student Peter Capaldi are among those who gave their backing to a £20m fundraising campaign to restore the structure.
Colin Grassie, chairman of The GSA Development Trust, said: "We are delighted with this significant boost from the UK Government, reflecting as it does the recognition of the reach and importance of The Glasgow School of Art.
"That enthusiasm has also been seen in countless donations and messages of support that we have received globally since The Mackintosh Appeal began.
"On behalf of the trustees, I would like to express our sincere gratitude."