Emergency services were called to the scene of the crash just south of Lockerbie and Annan near Junction 18 at about 4.45 am.
The crash involved a silver BMW and a grey Ford Kuga, and one man was pronounced dead at the scene.
Another man was taken to Dumfries and Galloway Royal Infirmary and was released after treatment.
The road was closed following the crash with local diversions in place.
However, it has since been reopened.
Sergeant Leigh McCulloch said: “Enquiries are at an early stage to establish the full circumstances surrounding this fatal road crash and it is important that we speak to any witnesses who were driving on the motorway around the time it happened.
“In particular we would like to speak to the driver of a grey Toyota who is understood to have passed the scene just after the incident occurred.
“We would also appeal to anyone else who was driving on the north or southbound carriageway around the time of the crash who may have seen either of the cars involved, or even witnessed what happened, to get in touch.
“Anyone with information is asked to contact the Divisional Road Policing Unit based at Lockerbie via 101 and quote incident number 0362 of Monday 12th June 2017.”