The two HGVs collided on the northbound carriageway near junction 50 for Ripon at 7am on Tuesday.
The wreckage then caught fire and large clouds of smoke could be seen.
Police have now confirmed that the man driving the articulated lorry died at the scene, but have not released his identity.
The carriageway is expected to be closed for the rest of the day and diversions are in place. Trapped traffic is still being released from the affected section.
Officers from the Major Collision Investigation Team are appealing for any witnesses who were travelling along that section of the road, who saw either vehicle prior to the collision, or anyone who may have captured dash cam footage to contact them.
Dial 101, select option 2 and ask to speak to Hamish Halloway. You can also email [email protected] quoting reference number NYP-22052018-0060.