The man, named locally as 31-year-old Lee Duncan, was found dead in his flat in Lauriston Place this morning.
John Farquar, 45, who lives in a hostel on Bruntsfield Place, said he and Mr Duncan had been “the best of friends” for almost two years.
He said he last saw the man five days ago when he visited him at the Lauriston Place flat.
Mr Farquar said: “I went round to see him today and saw all the police around the place.
“I shouted up to the window but the police told me he wouldn’t respond, I asked why and they said they couldn’t tell me any more.
“I know it’s him – it’s his flat that’s been cordoned on the second floor that the police are surrounding.
“I’m so gutted. We used to call each other ‘bro’ whenever we would see each other, I really can’t imagine what’s happened to him.”
It is understoood Mr Duncan was unemployed and living on income support.
Detective Inspector Matt Richards said: “Our inquiries are currently at an early stage, however we do believe the man’s death to be suspicious.
“We are appealing to anyone who was in the area this morning, who saw or heard anything suspicious, to contact police immediately.
“Similarly, anyone else who has any information that can assist our inquiries should also get in touch.
“At this time there are plans for extra patrols to be carried out in the area in order to provide reassurance to local residents, and officers are on hand to speak to members of the public if they have any concerns regarding the ongoing activity.”