Jay Burns, 20, was the driver of a car which left the road and hit a tree on the A710 road near Southwick on January 24.
Police today revealed that he died in hospital yesterday, Sunday.
Sergeant Jonny Edgar said: “Our thoughts remain with Jay’s family at this sad time.
“Our investigation is ongoing to establish the full circumstances of this incident and we would appeal to anyone who witnessed the crash or has any information that could assist with our enquiries to get in touch.”
Anyone with any information should contact Police Scotland on the 101 number, quoting incident 3354 of 24 January.
