As these dramatic helicopter images show, firefighters have been tackling the blaze, which started shortly before 12.30pm on Friday.
Chief Fire Officer Alasdair Hay said there were 17 units from Glasgow at the scene and specialist units from across the country.
He said the blaze was "significant" and had not yet been fully extinguished, but that teams were "confident" that the main fire had been dealt with.
He said: "At this point we can't establish what the cause is but we have specialist teams working with Police Scotland to establish the cause.
"We've had a significant fire within the building and at this point we're still extinguishing that fire.
"We've had firefighters inside working under very arduous conditions and at a later point we'll be able to determine and describe the conditions more fully.
"There has been significant spread within the building but we've used all our resources to bear on it.
"We regularly attend significant fires but the iconic status of this building is not lost on us."
Mr Hay said teams were trying to salvage the historic building.
He said: "Part of our operation is to try and salvage what we can and we worked with colleagues from the school who identified objects of significance that they would like us, if possible, to save.
"They described the objects and their location and we briefed officers and firefighters, where they could, did the salvage if it was safe to do so."
He could not say what objects were saved.
When asked if all student work has been destroyed he said: "It's too early to establish that. There was a salvage plan and we've worked to save the iconic items but we're not unaware of the importance of the work of students within that building.
"There are still pockets of fire but we are confident we have extinguished the main fire.
"There are structural engineers here and we are working with them to save as much of the fabric as we possibly can."
Muriel Gray, chair of the board of governors at the school said it had been a "devastating day".
She added: "We just want to make it clear that we are so grateful to the fire service who responded within four minutes and there were no casualties which is the main thing that we were concerned about.
"It's a very black day and we have a lot things to do and think about now.
"We are waiting for the investigation to be completed then we can start to rebuild some of the things that need done.
"Our thoughts are of course with the students whose degree shows were being prepared but I would like to say I have never been prouder in my life of an art school because the staff and students and the people of Glasgow have been fantastic.
"We don't know what's been destroyed and what's been salvaged so we're just waiting for the all clear so that we can get in and assess the damage. It's just a waiting game."