Police are appealing for witnesses as the driver, the only survivor of the incident, recovers in hospital from his injuries which are not believed to be life-threatening.
His two passengers, and man and woman in their 30s, were pronounced dead at the scene following the crash, which happened near Ilkley as the car travelled towards Otley, near Leeds.
A spokesman for West Yorkshire Police said officers were looking for witnesses to the crash which took place at around 3.30am on Denton Road in the village of Ben Rhydding.
“A Hyundai Coupé containing three occupants collided with a tree,” said the spokesman.
“A 35-year-old woman and a 32-year-old man were pronounced dead at the scene.”
The 37-year-old driver was detained at Leeds General Infirmary suffering from cuts and internal injuries.
The spokesman said enquiries into the incident and how the vehicle came to leave the road were still ongoing but it is understood not to be weather-related.
Those travelling in the car are all believed to come from the Ilkley area.
The two people who died have not yet been officially named by police investigating the crash who carried out detailed checks at the scene.
Their relatives are understood to have been informed about the tragedy yesterday.
Any witnesses to the crash or anyone with information about the incident are asked to contact West Yorkshire Police’s Major Collision and Enquiry Team on the non emergency number 101.
A 57-year-old man who had been treated in hospital since Monday after he apparently fell ill at the wheel of his car which went on to crash into a lamp post in Grimsby has died.
The man, who has not been named, had been treated in Diana Princess of Wales Hospital since the accident.