Officers were responding to reports of a man with a gun entering a bank and a bookmakers near Marloes Road, Scotland Yard said.
The suspect was then seen to enter a vehicle, which was stopped nearby at the junction of Kensington Road and Palace Gate just before 3.20pm.
“Shots were fired and a man sustained gunshot wounds,” a Metropolitan Police spokesperson said. Witnesses reported hearing three “loud bangs”.
The London Ambulance Service and London Air Ambulance were called to treat the man’s injuries, but he was pronounced dead at the scene at 4.08pm.
“Efforts are now being made to identify the man and to approach his next of kin,” police added.
The Met’s Directorate of Professional Standards has been informed of the incident, which has also been referred to the Independent Office for Police Conduct (IOPC).
The IOPC has confirmed it has begun an investigation, with a spokesperson adding: “After being notified of the incident by the MPS, we sent investigators to the scene and the post-incident procedure to start gathering evidence.”
Police have closed roads around the scene, close to Hyde Park and Kensington Palace, and advised people to avoid the area.
Pictures of the scene appear to show a taxi behind the police cordon next to a forensics tent. The Met said there was “no risk to the public” and the incident was not being linked to terrorism.