The 22-year-old had been involved in a collision with a taxi on Old Dalkeith Road, near the junction with Ferniehill Drive around 12.10am on Sunday.
Police continue to appeal for information following the incident, and would ask for anyone who may have been in the area at the time to come forward.
A police spokesman said: “We are still trying to establish the full circumstances surrounding this incident and are keen to hear from anyone who can assist with our enquiries.
“Motorists or pedestrians who remember seeing the man before the collision are asked to contact police immediately.
“We would also ask for the doctor who originally administered medical treatment to come forward and speak with officers.”
Anyone with any information should contact Lothian and Borders Police on 0131 311 3131, or the charity Crimestoppers in confidence and complete anonymity on 0800 555 111.