A property on Scotland Street is taped off this morning, with uniformed police outside and other plainclothes officers in attendance.
Forensics are attending.
A Police Scotland spokesperson said: 'Police in Edinburgh are investigating following the discovery of a man's body at an address in Scotland Street.
'The incident was reported to police at around 5.30am, Friday 2 December.'
'The death is currently being treated as suspicious'.
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UPDATE
The following press release was issued this afternoon.
Police in Edinburgh are appealing for information following the discovery of a body in suspicious circumstances at an address in Scotland Street.
The incident happened around 5.30am on Friday, December 2, when a disturbance was reported to police. Officers attended and the body of a man was discovered.
Enquiries are currently ongoing to establish the identity of the victim, however officers are currently treating the death as a homicide, pending a post mortem.
Officers are appealing for information and are asking for anyone who was in the area to come forward.
Detective Chief Inspector Keith Hardie of the Major Investigations Team said: “We have found a body in suspicious circumstances, which has sustained significant injuries.
“It is being investigated at the same level as a homicide, although until the result of the post mortem we cannot commit to this.
“With this in mind it is imperative that we trace those involved in this incident as soon as possible.
“I would urge anyone who was in the Scotland Street area on the morning of Friday, December 2, to get in touch with us immediately.”
Those with information can contact Police Scotland on 101 or anonymously through Crimestoppers on 0800 555 111.
UPDATE, 3 DECEMBER, 3.25pm
Police Scotland have arrested and charged a 28-year-old man following a death in the Bonnington area of Edinburgh.
Officers were called to an address in Scotland Street around 5.30am on Friday 2 December following a disturbance.
Entry was forced to a flat and the body of a man, who had sustained significant injuries, was found within.
Enquiries are currently ongoing to formally identify the man, who is believed to be in his early-thirties.
A post-mortem examination was conducted today (Saturday 3 December) and the death is being treated as murder.
The 28-year-old is expected to appear before Edinburgh Sheriff Court on Monday 5 December.
Detectives from the Major Investigation Team continue to conduct enquiries in connection with this death.
Anyone with information which may be able to help, or who was in the area around this time, is urged to come forward.
Those with information can contact Police Scotland on 101 or pass this anonymously to Crimestoppers on 0800 555 111.
UPDATE 6.12.16
Man named following death in Scotland Street, Edinburgh
Police Scotland can confirm the name of a 32-year-old man who died following a disturbance at an address in Scotland Street, Edinburgh.
He was Ashley Hawkins of Barry, Vale of Glamorgan.
Mr Hawkins died around 5.30am on Friday, December 2.
A 28-year-old man has been charged with murder in connection with his death. He appeared at Edinburgh Sheriff Court on Monday, December 5.
In a statement released through Police Scotland, Mr Hawkins' family said: "Our beautiful boy Ashley, we can't believe that he is gone. He was a loving son, brother and uncle and our hearts are now in pieces.
“He was helpful to everyone and was loved in his hometown of Barry. He will never be forgotten.”
Detective Inspector Stuart Alexander of the Major Investigation Team said: “This is a tragic incident and our thoughts are with Ashley’s family at this time.
“We are still conducting enquiries in connection with Ashley’s death.
“I would urge anyone with information which may be able to help, or who was in the Scotland Street area early on the morning of Friday, December 2, to come forward.”
Those with information can contact Police Scotland on 101 or anonymously through Crimestoppers on 0800 555 111.