Jaymie Stuart Hall suffered a number of serious injuries during a disturbance in Dumbryden Gardens, Wester Hailes, at about 21:25 on Saturday.
The 35-year-old was taken to the Royal Infirmary of Edinburgh but died a short time later.
The arrested man is expected to appear at Edinburgh Sheriff Court on Tuesday.
A 41-year-old man has been charged with murder following the death of a man in an Edinburgh street.