Liam Griffiths, 19, punched Blain Murphy as he chatted to a woman in the street and the blow caused him to fall to the ground.
Mr Murphy was taken to hospital and later had to have an operation leaving him with a metal plate and four screws inserted in his face.
Fiscal depute John Kirk told Edinburgh Sheriff Court today: "For absolutely no reason the defendant came up to the complainer and punched him once to the right side of his face.
"The complainer fell to the ground and the defendant walked away after committing this totally unprovoked assault."
The court heard Mr Murphy is expected to make a full recovery but the process would take some time.
Griffiths, from Christian Grove, Edinburgh, admitted punching Mr Murphy to the head, causing him to fall to the ground to his severe injury.
The attack happened at around 3.20am on 4 July last year at Edinburgh's North Bridge.
Griffiths also admitted breaching his bail conditions.
Defence agent Vincent Belmonte said Griffiths had very much changed his behaviour since the incident.
Sheriff Michael O'Grady deferred sentence until next month for background reports when further pleas in mitigation will be heard.