Robert Sharp, 50, from Maryhill in Glasgow, died in hospital following the accident which happened on the A74 (M) near Eaglesfield just after 16:00 on Wednesday.
Mr Sharp, a passenger in the car, was airlifted to hospital in Glasgow but later died from his injuries.
The 39-year-old driver, from Callander, was taken to hospital in Carlisle.
The collision involved a grey Peugeot 307 and a white Scania articulated lorry.
The 59-year-old lorry driver, from Reading, Berkshire, was uninjured.
Sgt Leigh McCulloch, from Police Scotland, said: "We would also be keen to hear from anyone who may have seen either the grey-coloured Peugeot 307 car or the white-coloured Scania lorry as they headed south prior to the crash."