The 51-year-old was found dying on the pavement outside a block of flats in Salisbury Road shortly after 3am yesterday.
Police are treating his death as “unexplained” and sealed off the street for much of the morning as a forensics team was called in.
Alarmed residents told how they woke to find officers in their street.
One neighbour said: “I didn’t see anything last night but I saw the police this morning.
“It’s shocking because this is a quiet street normally. You hear sirens going up Newington Road but not here.”
It was unclear whether the 51-year-old man lived in the flat or whether anyone else was in the property at the time.
Forensics officers were seen taking photographs in Salisbury Road while colleagues carried out further investigations inside the flat.
The road was later opened to traffic though police inquiries are ongoing as they try to discover how the man fell.
Police and paramedics were deployed to the scene at around 3.15am and found him critically injured in the street.
The man was taken to the city’s Royal Infirmary but was pronounced dead a short time later.
His death is the second fatal flats plunge in the Capital in less than a week after a man died while trying to clamber from the fourth floor of a Wester Hailes block on Thursday.
Residents watched in horror as he used a makeshift “rope” made from blankets tied together but lost his grip and plunged 40-feet at Cobbinshaw House South in Calder Gardens.
It was reported that the man made an escape bid after locking himself in a room at the property.
Police confirmed officers are investigating the Newington fall but have yet to determine any suspicious circumstances.
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.”
A post-mortem examination will be carried out to determine the man’s cause of death and find any clues as to how he fell.
The Police Scotland spokeswoman added: “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. [email protected]