The accident occurred on Ben Bank Road last Friday morning where the vehicle - which was displaying learner driver plates - collided with a tree.
A spokesperson for South Yorkshire Police said: ““We were called at around 9.10am following reports that a Volkswagen Transporter had collided with a tree on Ben Bank Road.
“The driver 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.”
Anyone with information is asked to call 101, quoting incident number 284 of May 20.