Ebrahim Aryaei Nekoo, from Edinburgh was found in Saughton Park at around 7.20am on Saturday.
The 41-year-old died as a result of his injuries and detectives launched a major enquiry to determine the circumstances surrounding this incident.
Chief Inspector Richard Thomas said: “Crimes of this nature remain extremely rare in Edinburgh, where crime rates continue to fall.
“Nevertheless, when they do arise, it can be of great concern to our local communities and it is important we respond appropriately.
“High-visibility patrols will continue in the Saughton Park area and officers will engage with local residents to offer reassurance to the community.
“Anyone who wishes to speak with police about any concerns they may have can approach these officers or contact their local policing team.”
The man is scheduled to appear at Edinburgh Sheriff Court today.