The force said a green Ford Fiesta crashed into a wall near Settle Golf Club at around 9.15pm.
The 18-year-old man in the passenger seat was pronounced dead at the scene. His family are now being supported by specially trained officers from North Yorkshire Police.
The 20-year-old driver of the car is currently in hospital with serious injuries.
A statement from police said: "Officers need to establish the circumstances surrounding the collision and are appealing to anyone who was in the area. Particularly those with dashcam footage travelling around the B6480 towards Settle around 9pm to contact them with information."
Anyone with information is asked to contact police on 101, or by emailing [email protected], quoting reference number 469 of December 3.