The pair, who lived in Morley, were travelling along the A65 near Austwick, Settle, when their car hit a tree on Sunday morning.
The passenger, 89, died at the scene and the 87-year-old driver passed away in hospital.
They were in a small, silver Nissan Micra heading towards Ingleton when the crash happened at around 10.45am.
Police are appealing for any witnesses to the collision, or anyone who saw the car travelling along the A65 prior to the collision to contact them, to help them establish the circumstances around the incident.
Contact North Yorkshire Police on 101, select option 2 and ask to speak to the Major Collision Investigation Team.