The man, believed to be in his 60s, fell from a bridge onto the Thornwood roundabout.
Police said he then suffered a heart attack and was taken to the Western Infirmary, where he later died.
Dumbarton Road was closed in both directions at the Sawmill Road Roundabout for some time after the incident.
Police were called to the incident around 1.50pm yesterday.
The man's identity will not be released until his family have been informed, police said.