Officers are appealing for witnesses after they were called shortly after midnight to Whetley Lane, near to the junction with Fairbank Road, in Manningham.
A grey Peugeot 107 was travelling along Fairbank Road towards the junction with Whetley Lane, officers said.
Another vehicle, a grey Vauxhall Astra, was travelling along Whetley Lane in the direction of Toller Lane.
The two cars collided close to the junction and then collided with two parked cars at the side of the road, police said.
A 20-year-old man was taken to Bradford Royal Infirmary but suffered fatal injuries and was pronounced dead at the hospital.
Anyone who witnessed the collision or has any information is asked to contact the police via 101, quoting log number 0040 of December 27.