Officers were called by paramedics at 8.55pm on Saturday, 11 January to Falcon Road, junction with York Road Battersea, pictured, following reports of a road traffic collision.
Two cars had been involved in a collision. A third party, a pedestrian aged in his 60s, was injured and pronounced dead at the scene.
One of the drivers, a 32-year-old man, left the scene on foot but returned a short time later.
He was arrested on suspicion of causing death by dangerous driving and failing to stop at the scene of a collision. He has been taken into custody.
The other driver, a 29-year-old man, was not arrested and is assisting police with their enquiries.Road closures were in place but have since been lifted.
Anyone who witnessed the incident, or who has information or dash cam footage that could assist police, is asked to call the Serious Collisions Investigation Unit at Merton on 0208 5435157.
Alternatively call 101 or tweet @MetCC, quoting CAD 6988/11 Jan.