Mr Stewart was married with two adult children.
The blue-and-white BMW motorcycle he was riding had been involved in a collision with a beige Skoda Octavia on Coldhill Lane on the outskirts of Sherburn-in-Elmet at about 1.45pm on Thursday.
He was airlifted to Leeds General Infirmary in a critical condition but died on Friday night, police said.
The driver of the Skoda, a man aged 26 from Leeds, who was arrested at the time of the incident, remains under investigation while inquiries continue.
North Yorkshire Police are re-appealing for any witnesses who have not already spoken to them, including anyone who saw either vehicle travelling between Lotherton Hall and Sherburn, to contact them.
Anyone with information is asked to call North Yorkshire Police on 101, select option 2 and ask for Traffic Constable Mark Mullins of the Major Collision Investigation Team at Tadcaster, or via email at [email protected]