The driver, who has not been named, was behind the wheel of a VW Transporter displaying L plates and being supervised by a 57-year-old man in the passenger seat.
The vehicle crashed into a tree in Silkstone Common in Barnsley on Friday.
South Yorkshire Police said: "Officers have launched an investigation following a fatal collision in Silkstone Common, Barnsley on Friday 20 May.
"We were called at around 9.10am following reports that a VW Transporter had collided with a tree on Ben Bank Road.
"The driver, a 22-year-old man, was taken to hospital and sadly died a couple of hours later. The passenger, a 57-year-old man, was uninjured.
"We are now appealing for any witnesses to the incident and the moments leading up to the collision. The investigation team would be particularly keen to trace the driver of a small car which is believed to have overtaken the Transporter prior to the collision.
"The Transporter was grey and was displaying L plates.
"Anyone with information is asked to call us on 101 quoting incident number 284 of 20 May. If you have dashcam footage, please email it to [email protected] quoting the incident number in the subject."