Thirty-two-year-old Rajon Chambers of Newark was pronounced dead at the scene early Saturday.
Katherine Carter, a spokeswoman for the Essex County Prosecutor's Office, said the pursuit began around 1:30 a.m., when police responded to an assault report.
As officers arrived on scene, Chambers left in his girlfriend's car. A short pursuit ensued, ending when Chambers crashed into a house. He then exited the car and ran off, but was struck by the cruiser.
The name of the officer driving the cruiser was not disclosed.
The prosecutor's office and Newark police officials will investigate the incident, which is standard policy for police-involved deaths.