Flames ripped through the celebrated Mackintosh building after it caught fire at about 23:20 on Friday.
The blaze spread to nearby buildings, including the Campus nightclub and O2 ABC music venue, which suffered "extensive damage".
There are not thought to have been any injuries.
Efforts to bring the fires under control were expected to be "prolonged", Deputy Chief Officer Iain Bushell said.
More than 150 firefighters were sent to the scene and were faced with "an extremely challenging and complex incident", he added.
Scottish Fire and Rescue Service deputy assistant Peter Heath said "pockets of fire" remained, but were under control.
He said the School of Art building had been "extensively damaged" and that all floors were affected.
"We remain firefighting in what is a very challenging situation," he added.
Firefighters have been pumping water from the River Clyde to tackle the blaze, resulting in a number of road closures in the area.
Insp Catherine McNally, of Police Scotland, praised the response of both the public and nearby licensed premises which were asked to evacuate.
Parts of Glasgow's Sauchiehall Street look normal for a Saturday morning. The rain falls heavily on top of chip boxes, the remnants providing breakfast for many a hungry bird.
But the presence of fire engines, police officers, bewildered passers-by and an acrid smell of smoke in the air indicate this is far from normal.
Smoke still billows from the Glasgow School of Art, the Campus nightclub and the O2 ABC venue, with all the streets around the area closed.
Once again, the people of Glasgow are watching on as one of its most famous buildings is on fire.
Once again, the words "so sad" are heard on every corner.
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