The Scottish Fire and Rescue Service was called to the scene at around 4.15pm yesterday afternoon at the abandoned building.
At its height, more than sixty firefighters were tackling the blaze to keep it under control.
Firemen remain at the scene this morning. It has been confirmed that there were no casualties.
A plume of thick black smoke could be seen billowing from the scene, with firefighters using a platform to hose down the flames from above. The smoke was visible for many miles.
A police presence was also in place on Craigleith Road to guide drivers past the site’s entrance.
Dozens of onlookers gathered nearby to watch the incident unfold, with one local resident saying their water supply had been shut off while the firefighters got to work.
One local resident, who did not want to be named, said he could see the blaze from his house.
He said yesterday: “It’s a huge amount of smoke and clearly it’s not out yet.
“It looks quite violent - it’s very black smoke.”
Another witness said the fire “raged all night”.
Nine fire appliances, one height vehicle and two water carriers were used at the scene.
Fire chiefs say they are now carrying out “dampening down operations”.
The old Royal Victoria hospital was shut in 2012 when a new unit opened at the Western General Hospital nearby.