The man was set upon by a gang of up to 15 youths, aged 14 to 16 years old, in an unprovoked attack as he was about to walk up the Waverley Steps to Princes Street.
The teenagers slapped and punched him until he fell to the ground as several of them filmed the attack on mobile phones.
The victim, who is thought to live in Edinburgh, was taken to the ERI where it was discovered he had a broken cheekbone.
His attackers fled along the pedestrian bridge in Waverley and ran off into Market Street.
The assault took place around 8pm on Friday. Police were today sifting through CCTV footage to see if they could identify the youths.
Detective Constable Mark Taylor said the victim was a quiet man who had been left particularly shaken by the attack.
He said: "The man was exiting the station, minding his own business, when he was set upon by the group coming down the steps towards the station.
"He was slapped on the head and back before being punched to the ground.
"It was a totally unprovoked attack and we are keen to speak to anyone who witnessed the attack or saw the group running off in the direction of Market Street. The station would have been still busy at that time and such a large group of youths running away would have stood out."
The speed of the attack and the number of youths involved meant the victim did not get a good description of those involved.
However, one of the group is described as wearing a grey hooded top and green and blue tracksuit trousers. He had short brown, gelled hair with a fringe.
Detective Chief Inspector Jim McKelvie, of British Transport Police, added: "This was a totally unprovoked and random attack leaving the victim injured and very badly shaken."
Happy slapping emerged in London in 2005 and quickly grew into a nationwide phenomenon.
Edinburgh's first happy slapping attack - in which the attackers seem to get a thrill from filming the violence - took place in June 2005 when two women were assaulted within minutes of each other in Holyrood Park.
Rail bosses have stressed that despite the latest attack, Waverley Station is generally a safe place.
Crime at the city's railway stations has been steadily reduced in recent years, with Waverley reporting a 13 per cent drop in recorded crime over the last year.
A spokesman for Network Rail, the owner of Waverley Station, said: "We were informed by the British Transport Police about an incident during which a young man was allegedly assaulted and we will do everything possible to assist with their investigation.
"We have been pleased to see a reduction in crime at the station over the last 12 months, so it is disappointing that such an incident has been reported at Waverley."