A 30-year-old was walking through Middle Meadow Walk at around 10.30pm yesterday when two men approached and confronted him.
One of the men then punched the victim in the face and continued the assault after knocking him to the ground before taking his belongings and running off.
The victim and another member of the public pursued the suspects to George Square and, with the help of an Edinburgh University staff member, followed the men until they jumped on to the railway track at Waverley Station before being lost to sight.
The first suspect is described as white, early to mid 40s, 5ft 11ins tall with an unshaven appearance. He was wearing a green jacket, a khaki-coloured hunting-style hat with earflaps, scarf, black trousers, gloves and was carrying a rucksack.
The second suspect is described as white, 6ft tall with a medium build, short cropped dark hair and was wearing a light-coloured jacket.
Detective Constable John McShane said: “Despite what must have been a very frightening experience for the victim, he was not seriously injured and continued to pursue his attackers as they made off from the Meadows.
“Given the distance the suspects have travelled, there are potentially many members of the public who remember seeing men matching their description make their way towards George Square and then on towards Waverley Station.
“We are currently reviewing local CCTV and working alongside British Transport Police and are keen to hear from anyone who believes they can assist with our enquiries.
“Anyone who can help identify these men is asked to contact police immediately.”
Those with information can contact Lothian and Borders Police on 0131 311 3131, or the charity Crimestoppers in complete anonymity on 0800 555 111.