It happened at around 12.20am on Penistone Road, Kirkburton.
The driver of a Vauxhall Corsa was travelling towards Huddersfield when the vehicle collided with an 18-year-old crossing the road.
The boy suffered fatal injuries and was pronounced dead at the scene.
The Vauxhall driver failed to stop at the scene and was found a short time later.
Two men in their thirties were arrested on suspicion of causing death by dangerous driving and a number of other offences believed to be related to the collision.
Both men remain in custody.
Road closures were in place, but the roads have since reopened.
Police are appealing for any witnesses to the collision or anyone that may have dash cam footage to contact the Major Collision Enquiry Team on 101 quoting log 0075 of 12/7.