The accident involved a blue Mazda Premacy and a white Ford Transit and took place near to junction 24 in Leicestershire at around 2am on Monday.
The elderly driver of the Mazda is believed to have been driving the wrong way along the carriageway before he crashed into the van. He died at the scene of the crash along with a 27-year-old man who was a passenger in the van.
Leicestershire Police said it had received reports of a car travelling the wrong way down the southbound carriageway of the M1 prior to the collision.
Anyone who has information about the incident or saw either vehicle prior to the collision is asked to call police on 101 quoting incident 23 of October 12 2015.