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 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.