The incident happened at around 12.45pm on the southbound stretch of the road where an articulated lorry carrying a dumper truck left the carriageway and went onto the verge.
Emergency services went to the scene and the driver of the vehicle was declared dead at the scene.
Police would like to speak to anyone who has information that will assist in the investigation of the crash.
The road closure caused major tailbacks of up to six miles at one stage.
A police spokesperson said: “Unfortunately the A23 was closed southbound for over four hours, but it is now open.
“This was necessary to safely facilitate the specialist recovery of the large vehicle and its load. We would like to thank the public for their co-operation and patience during this time.”