The cash will go to the Mackintosh Appeal, which aims to raise £20m, following the fire on 23 May which severely damaged the building.
The Scottish government has previously pledged £5m towards the fund, which has Hollywood star Brad Pitt and Dr Who actor Peter Capaldi among its trustees.
GSA estimates the cost of restoring the building to be between £20m and £35m.
Firefighters managed to save 90% of the iconic structure and 70% of its contents during a lengthy operation.
GSA believes eventual restoration work could take up to four years.
Chief Secretary to the Treasury Danny Alexander said he was "delighted" that the UK government would support efforts to return the Mackintosh building to its former glory.
He said: "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.
"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."
Professor Tom Inns, director of GSA, said the funding pledge from the UK government was "a huge boost" to the 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 from across the UK and the world," he said.
"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, bringing the UK's creative talent to the world and allowing the world to understand the unique contribution of Mackintosh."
The UK government is to donate £5m to help restore Glasgow School of Art's (GSA) fire-damaged Mackintosh building.