The 20-year-old who died was driving a Seat Leon which failed to negotiate a left-hand bend and hit a wall and railings outside Keighley Business Centre in Keighley.
The driver, from Stockbridge, Keighley, was pronounced dead at the scene.
A 15-year-old boy in the car suffered serious head injuries and two 16-year-olds, a girl and a boy, were also taken to hospital for treatment.
The 15-year-old was taken to Bradford Royal Infirmary but was later transferred to Leeds General Infirmary.
A police spokesman said the pursuit began at around 12.20am yesterday morning when an officer in an unmarked Vauxhall police car began to follow the Seat along South Street in Keighley.
The Seat used the forecourt of the Jet filling station to perform a U-turn and go back on South Street towards Keighley town centre.
The Seat failed to stop and "made off at speed" before the driver lost control on a bend and crashed, the spokesman added.
Investigations into the circumstances are now being carried out by the Independent Police Complaints Commission and West Yorkshire Police's Professional Standards Department.
The West Yorkshire Police Major Collision Enquiry Team is also investigating the crash.
Officers are seeking witnesses to the incident.
Anyone with information is asked to contact police on 0845 6060606.