The man, believed to be in his late 70s, suffered serious injuries after the incident at the junction of Eaton Square and Eccleston Street in Belgravia, Scotland Yard said.
Police were called to the scene at 6.45pm yesterday and the man was taken to hospital by ambulance, but later died. His next of kin is yet to be informed.
The driver of the taxi stopped at the scene but was not arrested.
Officers from the road death investigation unit are carrying out inquiries into the incident and anyone who witnessed the collision or has information is asked to call police on 0208 285 1574 or Crimestoppers on 0800 555 111.
We noticed today that the Evening Standard carried this story and yet they published not one word about a similar accident which occurred in Southwark Street SE1 last night. The incident in South London was between an Addison Lee Van and a pedestrian.
It would seem that the Standard is very apprehensive about stories which contain Private Hire vehicles. Very often, they refer to PH wrongly as Taxis, especially when it comes to sexual attacks on passengers.