An air ambulance, a road ambulance, two rapid response vehicles and a doctor were called to Gledhow Tower, Lincombe Drive, LS8, at about 1.42pm.
The man was treated by paramedics but was sadly pronounced dead at the scene.
A spokesman for West Yorkshire Police released this statement tonight:
"Police were called by the ambulance service to a report of a sudden death at Gledhow Towers, Leeds at around 1.42pm this afternoon.
"Officers attended to find the body of an adult man at the bottom of the flats following an apparent fall from an apartment.
"Initial enquiries are ongoing to determine the circumstances of what took place."