Police Scotland said the man was found critically injured on Salisbury Road at around 3.15am today (Tuesday).
It is thought he was taken to the city's Royal Infirmary but was pronounced dead a short time later.
A Police Scotland spokeswoman said: “Police in Edinburgh are investigating following the death of a man in Salisbury Road.
“The incident happened around 3.15am on Tuesday, April 23, when the man was found to have fallen from a third floor window.
“Police and emergency services attended and the man was taken to the Edinburgh Royal Infirmary, however he sadly passed away a short time later.
“Inquiries are currently ongoing and the death is being treated as unexplained. A report will be sent to the Procurator Fiscal.
“Anyone with information is asked to contact Police Scotland on 101, quoting incident number 0340 of April 23.”
For all the latest breaking incidents in Edinburgh - join our new Facebook group here.