The crash happened on Tivetshall Road, near Pulham Market at about 23:50 BST on Wednesday.
They have been named locally as Kyle Warren, Billy Hines and Dominic O'Neill and are believed to come from the nearby town of Harleston.
The teenagers died at the scene after the car left the road and crashed into the trees, Norfolk Police said.
The road is expected to remain closed for the rest of the day while investigations take place.
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Three teenagers have died after the car they were in ploughed into trees in Norfolk.