The 55-year-old man was pronounced dead at the scene.
Police have confirmed that the man fell from the third floor of Buchanan Galleries.
Police and ambulance staff - including a trauma team - were called to the incident at around 9.40am and shoppers were turned away from the main entrance, on Buchanan Street.
Inside, police tape cordoned off the area below the escalators on the ground floor.
Police and ambulance staff could be seen entering and exiting the building, and a stretcher was seen being carried into the building by paramedics.
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