More than 60 Lothian and Borders firefighters have been tackling the blaze after they were called shortly after 3pm.
There are 11 fire engines and height appliances at the scene.
No-one is understood to have been trapped or injured - many having been evacuated.
Traffic diversions are in place in the surrounding area, including Princes Street, to allow fire crews to tackle the blaze.
It is thought the blaze started in the Thomas Cook shop on the ground floor.
A spokesman for Lothian and Borders fire and rescue said: “We were called to a ground floor property fire, which quickly spread throughout a four-storey building, and into the roof.
“We are not aware of anyone involved in the fire, but we are checking the buildings adjacent.”