The 76-year-old man was taken to Leeds General Infirmary with serious injuries on Saturday and died in the early hours of yesterday morning.
The driver of the other vehicle, a 37-year-old man from Leeds, remains hospital with serious injuries.
Police today released details of the incident as they urged any witnesses to the crash to come forward.
A spokesman said the deceased man, who is not being named at this time, had been driving a dark coloured Toyota Corolla on the A64 westbound carriageway in the direction of Leeds.
The car crashed with a green Mercedes A class near the junction with Grimston Bar at about 6.20pm.
The spokesman said: "It is believed the Corolla had been travelling in the wrong direction on the A64 when the collision occurred.
"As a result of the collision the drivers of both vehicles were taken to Leeds General Infirmary with serious injuries.
"Unfortunately the driver of the Toyota Corolla, a 76-year-old local man died in the early hours of Sunday morning."
The road was closed while emergency services helped the injured drivers and collision investigators examined the scene.
It reopened at around 12.30am on Sunday.
Police are now appealing for witnesses who saw the collision or either of the vehicles beforehand.
Contact North Yorkshire Police on 101, select option 2 and ask for the Major Collision Investigation Team at Tadcaster Police Station or email [email protected]
Anyone making contact is asked to quote ref 12160218502.