The collision involving a pedestrian and a bus happened on Saturday at around 5.35pm in Haymarket Terrace.
Emergency services were called to the scene, but the 79-year-old man died at the scene.
Sergeant Barry Sommerville, from Edinburgh’s road policing unit, said: “Our thoughts go out to the family and friends of the deceased at this time.
“We are carrying out an investigation to establish the full circumstances of this incident and would appeal to anyone who was in the Haymarket Terrace or Clifton Terrace area at the time of the crash to come forward.
“If you have any information or a potential CCTV footage that could assist our inquiries, please call police on 101 quoting incident 2828 of February 4.”