Officer say a heavy goods vehicle was travelling towards Longtown when it crossed on to the opposite side of the road before leaving the carriageway.
The 48-year-old driver, who is thought to have suffered a medical episode, was found to be unresponsive at the scene.
He was taken to the Cumberland Infimary in Carlisle where he died.
The busy cross-border road was closed for four hours to allow for recovery of the vehicle. No other vehicles were involved in the incident.
Police are appealing for any witnesses who have not already made themselves known to Cumbria officers to contact them on the 101 telephone number.