Robert Provis, 41, from the Halifax area was involved in the incident at 9.07pm on Saturday (September 29).
The collision took place on Aachen Way at its junction with Skircoat Moor Road at King Cross, near Halifax Fire Station, and involved a black Renault Megane motor car and a pedestrian.
The driver of the involved vehicle failed to stop at the scene and the car involved was later found abandoned nearby.
The driver later presented himself to officers and he was arrested on suspicion of causing death by dangerous driving. He has been released pending further investigations.
Officers are appealing anyone with any information on the incident to contact police.
Police would especially like to hear from anyone who witnessed the collision, or anyone who saw the Renault Magane driving in the Halifax area prior to the collision. Also from anyone that may have dash cam footage of the vehicle driving on then date in question.
Anyone with information is asked to contact the Major Collision Enquiry Team on 101 or via the online chat facility, quoting log number 1937.