Police appealed for witnesses to the incident which happened in Jackson's Entry at about 22:30 on Thursday.
A 19-year-old man had taken his wallet from his pocket as he looked for a cash machine when two men ran towards him from behind.
The pair knocked the man to the ground and punched him in the face before stealing his wallet and running off.
The first man was white, in his early 20s and about 5ft 8in or 5ft 9in tall, of skinny build, with a very pale complexion.
He had small stumpy brown teeth and a receding hairline forming a v-shape on his forehead. He also had blue eyes and black stud earrings in his ears. He was wearing a grey cotton Adidas tracksuit.
The second man was white with a tanned complexion, of athletic build and had dark spikey hair and sunken eyes.
He was wearing Puma jogging bottoms and a black hooded top with a gold zipper.
Det Con Iain Wallace from Police Scotland, said: "This was a very distressing incident for the victim, though, thankfully he did not sustain any serious injuries."
He appealed for anyone with information to contact police.

Hull and Humber Chamber of Commerce said the 33ft (10m) stainless steel sculpture next to Hull's Beverley Gate relic was like a "granny's vase".
The gate was where King Charles I was refused entry to Hull in 1642, sparking the English Civil War.
Hull City Council said it has submitted plans for "an engaging piece of art".
The chamber is to request the council reconsider the plan.
Live updates on this story and others from Hull and East Yorkshire
The statue, called Shadow Gate, is to be positioned between Whitefriargate and King Edward Street.
Architects Tonkin Liu said it "invokes the imagery of the trading ships masts and sails," and that "careful consideration has been made to position the sculpture to minimise any harmful impact to surrounding historical buildings."
Beverley Gate was designated a scheduled ancient monument earlier this year.
The chamber has suggested, as an alternative, a statue of Sir John Hotham - the governor of Hull who refused King Charles I entry into the city and its arsenal.
During the civil war he was found guilty of treachery and executed in London.

3 February 2015 Last updated at 17:47 GMT
He's been in prolific goal scoring form for Derry City and by the time he tucked himself into bed on Monday night, the transfer window had closed and Michael Duffy was living his boyhood dream.
He will be moving to Celtic after passing a medical and agreeing personal terms with the Scottish champions.
BBC Newsline's North West reporter Keiron Tourish has more.
A man has been punched and robbed in an Edinburgh Street by two men, one of whom had stumpy brown teeth.
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Plans for a sculpture near the remains of Hull's ancient defence walls have been criticised by the chamber of commerce.
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He's 20 and a Northern Ireland U21 international.