Officers were called at around 2.34am to reports there was a vehicle driving eastbound on the westbound carriageway of the M62 near to junction 26 at Huddersfield, the force said.
A spokesman said they were called again shortly after and told there had been a two-vehicle crash.
“Officers have responded and located the two vehicles. Two males in one of the vehicles, which is a white Skoda, were declared deceased at the scene,” he said.
“A male, believed to be the driver of the second vehicle involved which is a black Vauxhall Insignia, was arrested for causing death by dangerous driving.
“He also failed a roadside breath test ... the major roadside collision team are continuing the investigation.”
The force said the two men killed in the collision were 34 and 37, and that the 22-year-old man who was arrested is currently being questioned by officers.