The 26-year-old victim was walking on the footpath which runs between Hailesland Road and Harvesters Way in Wester Hailes when he was approached by the suspects.
They told the victim they had a knife, and forced him to hand over a small sum of cash. The pair then ran off down Harvesters Way and through the underpass that leads to the Murrayburn area.
The incident happened at around 6pm on Sunday.
Both suspects are described as white, in their mid to late teens, around 5ft 9in tall, and wearing dark clothing.
A police spokesman said: "Although the victim wasn't injured, he was understandably distressed as a result of his ordeal, and we are appealing for anyone with any information that can help police identify the two suspects to come forward.
"Anyone who witnessed the robbery, or who was in the area at the time and saw the suspects there, should contact police immediately.
"Similarly, anyone who recognises their descriptions should also get in touch."
The spokesman appealed to anyone with any information to contact police on 0131-311 3131, or Crimestoppers on 0800 555 111.