The man is believed to have been left trapped while dismantling the lift at Prince William House, 21 Queen Street, in the city centre.
He was part of a team working on the redevelopment of the four-storey building.
Fire crews, paramedics and the police were called shortly after 11am today.
Watch manager Ross Philips, from Gipton fire station, said: “The ambulance had arrived first and by the time we got there the incident had already happened and there was nothing more that we could do.
“Our job was to make the area safe, work with police to keep people away from the area and inform the Health and Safety Executive.”
Built in 1983, Prince William House – the former offices of Irwin Mitchell solicitors – was bought by private investment company Formal Investments in 2010.
Planning permission was granted last year to add two new floors. Work started shortly afterwards.
Quarmby Construction was contracted to carry out the building project.
A spokeswoman for the company said: “The police and the Health and Safety Executive have been informed and are now investigating.
“No additional information will be given or comment made regarding this incident until further notice.”