Victim Liam Maloney was attacked in Niddrie Marischal Road, near the junction with Niddrie Marischal Grove, at around 8pm on Thursday.
The 30-year-old was taken by ambulance to Edinburgh’s Royal Infirmary, where he died on Saturday.
A police spokesman said a post mortem examination as been carried out and that Mr Maloney’s death is being treated as suspicious.
He added that the victim’s relatives had been made aware and that a report would be sent to the Procurator Fiscal.
Detective Chief Inspector Frank Travers, of the Major Investigation Team, said: "This appears to have been a targeted incident and we do not believe there is any risk to the wider public.
"Extensive police enquiries are ongoing at this time and officers are gathering CCTV footage from the surrounding area.
"Door to door inquiries are also being carried out.”
He added that there would be a ‘continued police presence’ in the area while enquiries are carried out.
"I would like to reassure the local community that everything is being done to trace the person responsible,” he said.
Anyone who was in the area at the time of the assault or who has CCTV, dashcam or other footage is asked to get in touch via an online portal.
The portal can be accessed at https://mipp.police.uk/operation/SCOT22S13-PO1 and information can be provided anonymously.
Witnesses can also call 101 quoting reference 3262 of May 5.