Police said Christopher Narayan Blair (32), of Dunedin, died at the scene of the crash in Wansbeck St at about 7am on Saturday.
Oamaru firefighters spent about half an hour cutting a person out of a damaged car after the single-vehicle crash.
Emergency services said earlier that a second person was flown to Dunedin Hospital on the Otago Regional Rescue Helicopter.
Police received a report about 6.30am of a vehicle driving dangerously on State Highway 1 south of Oamaru.
Shortly before 7am, a police unit spotted the vehicle in the Alma area and attempted to stop it, a police spokesman said.
The driver fled, and officers followed for a short time before abandoning the pursuit.
The vehicle was then located crashed at the intersection of Severn St and Wansbeck St in Oamaru.