The accident happened at Buchanan House on Port Dundas Road at midday Wednesday.
Another man has been taken to the Royal Infirmary suffering from “severe head injuries”, the Scottish Ambulance Service said.
The boom of the 43 metre work lift buckled bringing the workers crashing to the floor.
The victims were fixing safety netting on the site as part of ongoing refurbishment work.
The dead man has been named by police as Gareth Currie, a 39-year-old from Baillieston.
He was employed by safety netting contractor One Stop Safety Systems while the injured man worked for Craig Services and Access Ltd.
The machine involved is believed to be a Bizzocchi 43m cherrypicker.
One eyewitness told the Daily Record: “I saw the two guys up in the basket about an hour earlier.
“One of them will have been operating the cherry picker and the other will have been the contractor who was working on the building.
“So far as I know, it is the contractor who has died and the cherry picker operator was injured.
“I heard a massive bang at around 12.30 when the basket hit the ground. The police and ambulance were on the scene within minutes.
“My heart goes out to the family of the man who was killed.
“I would imagine the health and safety investigators will be all over this one because the crane has just snapped in two.
“It looks like some pins inside the arm have snapped and the thing has just buckled.”