Paul McGlade, 35, from Edinburgh, was struck by a black Mercedes A class car on Colinton Road around 11.35pm on Saturday July 30.
The 20-year-old male driver of the car was uninjured.
Mr McGlade was taken to the Royal Infirmary of Edinburgh where he died on Tuesday.
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Police Scotland Sergeant Paul Ewing said: “Our thoughts are with Paul’s family and friends at this difficult time.
“Our enquiries are ongoing to establish the full circumstances which led to this incident and I would urge anyone who may have information but has not yet spoken to an officer to get in touch.
“Anyone with information can call 101, quoting reference 4406 of Saturday July 30 2022.”