The 66-year-old pedestrian was hit by a van near a row of shops in Croydon on Friday evening.  He died at the scene.
The van did not stop after the crash, but a 34-year-old man later handed himself in, the Met said.
He has been arrested on suspicion of failing to stop at the scene of an accident and causing death by dangerous driving. He remains in custody.
Detectives have appealed for witnesses to the incident, which happened at about 17:45 GMT at the King Henry's Drive junction and Calley Down Crescent in New Addington.
A man has died after being knocked down in an alleged hit-and-run in south London.