Michael Strong, 30, died on October 16 following the crash involving a silver Vauxhall Corsa on Middleton Road, Morley.
Police said he was walking with another man along the road, near the junction with Clough Street, when it happened at 10.40pm.
Mr Strong, from Morley, was taken to hospital after the crash, in which he suffered serious injured, but a West Yorkshire Police spokesperson today confirmed he has now died.
The spokesperson said: "Police can now confirm the pedestrian was 30-year-old Michael Strong, from Morley.
"The silver Corsa initially left the scene of the collision but the driver returned about 30 minutes later and the 29-year-old male driver was arrested on suspicion of causing serious injury by dangerous driving.
"The vehicle was recovered nearby and the driver was released from custody pending further investigation."
Police are now appealing for anyone with footage of the crash, or who witnessed the collision, to come forward.
Anyone with information is asked to contact the police via 101, quoting reference 13170481545.