The men, believed to be foreign nationals, were hit by the marked car shortly before midnight on Friday, Bedfordshire Police said.
They were believed to have been making their way home after a night out when the car mounted the pavement on a residential street.
A force spokeswoman said the police car, which had been responding to an incident, struck the pedestrians as it left the road after colliding with a Vauxhall Zafira.
The collision happened at the junction of Holland Road and Leagrave Road in Luton.
A police spokeswoman said: "Two pedestrians have died following a collision with a police car which was responding to an incident in Luton.
"As a result, Bedfordshire Police have voluntarily referred the investigation and control of the incident to the Independent Police Complaints Commission, which is standard procedure under such circumstances."
She added: "The marked panda car, crewed by two male police officers from Luton, was responding to an immediate call for assistance and was on blue lights and a siren when it first collided with a Vauxhall Zafira being driven by a man who was alone in the car.
"The police car then left the road and collided with two men, believed at this time to be foreign nationals, who were standing on the pathway at the junction of this road and who were both killed."
Police said attempts to identify the pedestrians and contact next of kin were under way.
The police officers involved and the driver of the Vauxhall Zafira were uninjured.
The scene of the collision remained closed yesterday as investigations were carried out.