It happened on the Meenacloy Road in Castlederg on Sunday, May 31.
Detective Inspector Michael Winters said: “The man who sadly lost his life in the collision was 21 years old and was the rider of an orange Kawaski motorcycle.
“It is believed that this motorcycle was in collision with a black BMW jeep at around 11am on Sunday morning.
“The BMW failed to stop following the collision and is believed to have driven on towards Ederney.
“I would firstly like to ask the driver of the BMW to examine their conscience and to come forward to police to explain what happened.
“It is likely that the BMW would have sustained damage due to the collision and I would therefore like to speak with anyone who is approached to repair this vehicle.
“I would also appeal to anyone who was travelling on the Meenacloy Road at around 11 am on Sunday and witnessed the collision, or who may have captured dash-cam footage of it, to contact police on 101, and quote reference 958 of 31/05/20.”
The name of the victim has not been released at the request of his family.