Glynn Barton, chief operating officer of Transport for London (TfL), confirmed the “deeply distressing incident” happened at around 9am on Monday 29 January.
Reports suggested a Number 13 double-decker bus crashed into a shelter at the busy transport hub.
Land and air ambulance crews battled to save the pedestrian but they were declared dead at the scene.
The bus driver was taken to hospital.
Police are working to trace the pedestrian’s next of kin.