The incident happened yesterday around 3am on Sunday 7 October on George Street.
A 25-year-old man had been in the Le Monde nightclub and was standing near the Hard Rock Café when a male approached and punched him in the face. The suspect then made off and the victim also then left the area with friends.
An ambulance, which had been called by members of the public who witnessed the attack found the injured man on Rose Street and he was taken to hospital for treatment on a broken jaw.
Officers are now keen to speak to anyone who can assist with their enquiries into this assault.
The suspect is described as white, over 6ft tall, between 20 and 25 years-old with a slim build and short fair hair spiked at the front. He was wearing a checked shirt, dark skinny jeans and dark shoes.
It is believed he was with another male who was similar in age, but was shorter and wearing a t-shirt with light-coloured stripes, blue jeans and white trainers.
Detective Constable Graham McIlwraith said:- “We are currently still trying to determine the full circumstances surrounding this attack.
“Given the time at which this incident took place, there were potentially a number of people leaving the various establishments in George Street who may have seen something suspicious.
“Anyone who witnessed the assault or who can help identify the male responsible is asked to contact police immediately.”
Anyone with any information can contact Lothian and Borders Police on 0131 311 3131, or the charity Crimestoppers in confidence and complete anonymity on 0800 555 111.