A 78-year-old Brighton man died after the collision in Brighton at around 10pm on Tuesday (January 10).
A Vauxhall Astra had failed to stop for police before a chase ensued, officers said.
Officers pursued the car before the Vauxhall was in collision with a 78-year-old pedestrian who died at the scene in Kemp Town. The car was found abandoned soon after on Madeira Drive near Concorde 2, according to police.
Sussex Police said a 33-year-old man from Brighton was arrested when he handed himself in to police on Wednesday morning (January 11) in connection with the collision.
He was arrested on suspicion of causing death by dangerous driving, drink driving, failing to stop for police and failing to report an accident.
On Wednesday afternoon, a second man handed himself into police. The 35-year-old was also arrested on suspicion of causing death by dangerous driving, drink driving, failing to stop for police and failing to report an accident. Both men remain in custody.
Sergeant Richard Hornsey said: “This is a tragic incident and our thoughts are with the family of the victim at this time.
“We continue to appeal to anyone who saw what happened or has any other information to contact police here quoting Operation Beresford.”
Police watchdog the Independent Police Complaints Commission (IPCC) has been informed and has begun an independent investigation into the circumstances of the police pursuit.
An IPCC spokesman said: “The Independent Police Complaints Commission (IPCC) is independently investigating the circumstances of an incident in Brighton in which a pedestrian was fatally injured.
“The incident happened at around 10pm last night, when a Vauxhall Astra apparently failed to stop for a marked Sussex Police car.
“Shortly afterwards the Vauxhall Astra collided with a pedestrian at the junction of St James’ Street and Old Steine, Brighton. The pedestrian died at the scene.
“The IPCC investigation will examine the actions and decisions of the police officers who were in the area at the time. The officers have provided their initial accounts of the incident, and we are in the process of obtaining CCTV footage and other relevant evidence which will help to establish the sequence of events.”