Poliuce said officers were on patrol in Hyde, Greater Manchester, at 12.50am on Monday when a red Volkswagen Golf failed to stop for them.
A chase ensued but officers lost sight of the vehicle.
When the car was found a short time later, it had been in collision with an oncoming blue BMW in Manchester Road and had then crashed into a building.
The driver of the Golf, the only occupant of the car, died at the scene.
It is not yet known why police started the chase.
The driver and passenger in the BMW were taken to hospital with injuries which are not believed to be life-threatening.
Superintendent Chris Allsop, of GMP, said: “The family of the man who sadly lost his life have been informed and are being supported by family liaison officers.
“The incident has been referred to the Independent Office for Police Conduct by GMP’s Professional Standards Branch in line with normal policy.
“The IOPC are independently investigating the circumstances of this incident and GMP will fully support this investigation.”
THis morning the scene remains cordoned off with officers standing guard.