The incident happened at about 17:20 on the eastbound carriageway of the city's West Approach Road.
A female passenger who also fell from the motorbike was uninjured.
The carriageway remains closed while police officers carry out crash investigation work. Police Scotland urged anyone who saw the incident to come forward.
In particular, officers want to trace a male cyclist who was seen in the area, having joined the West Approach Road at its junction with Roseburn Street.
Insp Brenda Sinclair, of Police Scotland, said: "Tragically, a man has passed away as a result of this incident and my thoughts are with his family at this sad time.
"Our inquiries into this matter are ongoing and I ask anyone with relevant information to contact police on 101.
"I also appeal directly to the male cyclist to contact police immediately."
A 52-year-old man has died after crashing his motorbike on an Edinburgh road.