The drama began at around 3.15pm on Sunday as plumes of smoke spread from the rear of the old Royal High School building across the east end of the city.
Four fire appliances were sent to the scene with emergency services cordoning off the area and advising people to move away due to the smoke. There were no reports of injuries but crews stayed on the scene to dampen down.
The cause of the blaze is not yet known.
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“Wishing all the best to the emergency services at the scene.”
An eyewitness at the scene has said that they have been told police would be evacuating the area.
The fire service said they would not be leaving the scene until it is completely extinguished and made safe.
Another eyewitness added: “The ground is very dry, plus very windy and changing direction which meant the fire spread. There were lots of folk about too, enjoying nice day and amazing views.
"But people are being warned to stay away because of danger from smoke inhalation.”