The scheme will help give students studio time to develop new work and rebuild their portfolio following the blaze at the world-renowned building on Friday.
First Minister Alex Salmond also announced that funds raised by the institution to restore the building to its former glory will be matched by the Scottish Government, with up to £5 million being offered.
About 200 firefighters were involved in tackling the blaze at its height and the fire service has been widely praised after crews salvaged 90% of the structure and saved up to 70% of its contents.
As well as housing one of Europe's leading art schools, the listed Mackintosh-designed building is a tourist attraction in its own right.
Completed at the turn of the 20th century, it was voted as the best building of the past 175 years in a poll by the Royal Institute of British Architects (Riba).
Professor Tom Inns, director at the art school, said: "The beating heart of the GSA is its students and our priority is to ensure that all those most seriously affected by the fire are given the opportunity to rebuild their practice.
"The GSA will therefore create special bursaries which will enable the students have sufficient studio time to develop their practice and make new work."
Mr Salmond also announced that ministers would work with GSA to develop the bursaries scheme.
He said: "The Mackintosh Building of the Glasgow School of Art is truly unique and last week's fire was a devastating blow for students and staff as well as the wider arts and architecture community worldwide.
"The very severe damage to the building's iconic library, in particular, is a cultural loss of significant magnitude.
"The Mack is an extraordinary building. It is an architectural gem and the artistic heart of Glasgow. It can and will be restored, and everything which can be done must be done to deliver this."
The funding announcement comes as a team of 35 specialist conservation staff from Historic Scotland have been sent to the building as part of the salvage operation.
The main part of the damage caused was in the 1907- 09 part of the building, including the loss of the unique library.
However, the 1897-99 part of the building has survived intact, including the Mackintosh Museum, Mackintosh Room, the director's office and studio, boardroom and furniture gallery.
The archives have also survived.
A joint investigation between the fire service and Police Scotland is working to identify the cause of the blaze.
Final-year students had been preparing for their end-of-year degree show when the blaze broke out.
GSA said an enhanced fire suppression system was due to be completed at the building over the summer but did not include standard sprinklers because of the potential risk of water damage to artefacts.
During topical questions at Holyrood today, Culture Secretary Fiona Hyslop was asked if there were plans to review the fire risk at other historic buildings.
Glasgow Labour MSP Drew Smith said: "We don't know if a more advanced fire prevention system would have been of great assistance in this case, but it is of course a tragic irony that that work was planned but hadn't been completed before this fire broke out."
Ms Hyslop responded: "I can confirm that the GSA building had appropriate fire protection for a grade A listed building, although it is always difficult to ensure an appropriate system.
"They were doing the right thing in implementing that but clearly in terms of the interruption over the period for understandable reasons that had not as yet been completed.
"Historic Scotland are constantly working with those in the heritage aspects. Many of them are privately-owned buildings, it's not just those that are in the public sector or under the protection of government agencies so that is under constant review.
"But I am absolutely clear that GSA have always been very conscious of the risk. Unfortunately that risk was realised over the weekend."