The 36-year-old victim had been walking on Forrester Park Loan heading towards Broomhall Road at around 5.40am.
As he walked he noticed two men walking towards him heading from Forrester Park Drive.
The two suspects engaged the man in conversation on before launching an unprovoked attack, which resulted in the victim sustaining serious leg injuries.
The attackers then fled the scene on foot. They are believed to have headed back along Forrester Park Drive in the direction of Broomhall Road.
The man was taken to the Royal Infirmary and later discharged after treatment.
The first suspect is described as white, in his early 20s, around 6ft tall with cropped dark hair and had a strong smell of alcohol. He spoke with a Scottish accent and wore a brown hooded top and grey-coloured jogging bottoms.
The second male is white and in his 20s, has a medium build, around 5ft 10ins tall and wore a black top with the hood up and dark jogging bottoms.
Detective Constable Gavin Howat said: “From our initial inquiries this appears to have been an unprovoked and cowardly attack.
“We are now carrying out a thorough investigation into this matter including reviewing the local CCTV network and carrying out door-to-door enquiries.
“Today I want to hear from anyone who was in the area of Forrester Park Drive in the early hours of Tuesday and who saw these men.
“I’d also encourage anyone who recognises the description of the attackers or who have any information that can assist with our investigation to come forward immediately.”
Those with information can contact police on 101 or alternatively the charity Crimestoppers anonymously on 0800 555 111.