Officers were called to reports of a man with a firearm seen to enter a bank and bookmakers in Marloes Road, west London, shortly after 3pm, Scotland Yard said.
The man was then seen to get into a vehicle and leave the area.
At 3.19pm, armed officers stopped a vehicle at the junction of Kensington Road and Palace Gate, the Metropolitan Police said. Shots were fired and a man sustained gunshot wounds.
Witnesses reported hearing three loud bangs.
The emergency services were called and the man was treated at the scene, but he was pronounced dead at 4.08pm, the force said.
Efforts are under way to confirm the man's identify and inform next of kin.
The Met said its Directorate of Professional Standards has been informed and the incident has been referred to the Independent Office for Police Conduct.