Brandon Frew, 19, Caelan Megson, 21, Matt Walshaw, 18, and Declan Grove, 19, died in the incident on the A6120 in Horsforth on Saturday, June 30.
Coroner Kevin McLoughlin told family members of the men, present at the hearing this morning, that he felt for all of them as he begun their inquests today.
He said: "It's my sad duty this morning to open the inquests touching four young men who died in a road traffic accident."
The hearing, at Wakefield Coroner's Court, was told the collision, which occurred at around 2.40am, involved a Seat Leon and Seat Alhambra private hire vehicle.
Mr Megson, of Stanhope Drive, Horsforth, was understood to be the driver of the Leon, which had six occupants, the court heard. The plasterer's death was confirmed at the scene at 3.05am.
Mr Frew, a labourer of Broadgate Walk, Horsforth, was understood to be a front seat passenger in the vehicle. His death was confirmed at 3.10am.
Addressing members of his family present in court, Mr McLoughlin said: "I offer you my profound sympathy."
Mr Walshaw and Mr Grove were both believed to be rear seat passengers.
The death of Mr Walshaw, an apprentice builder of Rose Avenue, Horsforth, was confirmed at 3.22am. Family members of apprentice plasterer Mr Grove, of Outwood Lane, Horsforth, who were present in court, heard his death was recorded at 3.15am.
Speaking to family at the hearing, Mr McLoughlin said: "Thank you very much for attending court and I feel for all of you, I really do."
The inquests were adjourned pending further enquiries.
Two girls, aged 16 and 17, who were also in the car, were seriously injured and taken to hospital.
The 42-year-old taxi driver from Bradford was also hurt.