The pursuit took place shortly before 2pm in the coastal suburb, with police confirming the pursuit took place on Hawke St.
Unichem Pharmacy manager George Mansour said they heard the sound of a police chase and moments later saw someone on the ground.
He said a little while later a police officer came into the store to tell them someone had passed away.
Acting Canterbury District Commander Mike Johnson said a pursuit was initiated after a person of interest failed to stop for police.
However, it was abandoned due to the manner of the driving.
Sam Heselwood was working nearby on Pages Rd when a man wearing a grey hoodie sped past in a Subaru Legacy wagon with a police car in pursuit.
Shortly afterwards, the same car sped back the other way "going 200km/h at least", with eight or so police cars behind him, Heselwood said.
Again, several minutes afterwards, the same man, now in a van, drove back in the other direction.
Video footage from the scene shows the van screaming down the road, mounting the kerb and almost hitting a pedestrian who narrowly ran out of the way.
The police officers had by that point appeared to have pulled out of the pursuit, Heselwood said.
Johnson said the vehicle was located shortly after the chase was abandoned and two of three suspects were arrested without any troubles.
"Shortly afterwards the third occupant stole a nearby vehicle and rammed a police dog van," he said.
"Soon after the stolen vehicle collided with a pedestrian at the intersection of Hawke St and Shaw Ave, New Brighton."
As a result of the collision, the pedestrian died and inquiries are underway to locate the driver of the second fleeing vehicle.
"Police are currently working to identify and notify next of kin. The road is closed and the serious crash unit is at the scene," Johnson said.
"The full circumstances are being investigated by police and the IPCA will be notified. I am unable to provide any further details at this time."