The incident happened just after midday at Saughton Mains. Witnesses reported seeing CPR being given to the man.
Police have confirmed that the man has died.
Edinburgh Trams stated a “serious accident” at Saughton Mains had caused partial closure of the route.
A witness on the scene said a body was seen lying in the grass and a tram driver was nearby “in shock” as a passerby gave CPR.
There are several delays in the area due to the ongoing emergency response.
A spokesman for Edinburgh Trams said: “We can confirm emergency services were called to a location near the Saughton tram stop at around 12.10 this morning following an incident involving a pedestrian and a tram. “An investigation is currently underway and until it is completed we are unable to comment further.”
Trams continue to run between Haymarket and York Place.
Trams are expected to be subject to cancellations or delays until 4pm.