66-year-old Ian Hudson died following the collision on Manchester Road at around 2.30pm on Friday, July 5.
The black Lambretta scooter driven by Ian collided with a yellow Mercedes van at the junction with Rivelin Valley Road.
Ian was taken to hospital, where he died shortly after his arrival.
His heartbroken family have paid tribute to him.
They said: “We are devastated at the loss of Ian. He was a friendly and outgoing man with many friends across Sheffield.
“He had ridden scooters and motorbikes for many years. In retirement he would regularly drive out to the Peak District with friends, with the Fairholmes Visitor Centre at Derwant Dam a frequent destination.
“He was also an active member of Sheffield Aces Scooter Club.
“We are trying to come to terms with the fact that he is no longer with us and would encourage anyone with any information to please come forward.”
The family are being supported by specialist officers and have asked for their privacy to be respected.
A spokesman for South Yorkshire Police said: “Officers echo Ian’s family’s request for anyone who saw what happened to get in touch, especially any motorists who were travelling along the A57 with dash cam footage.”
Manchester Road was closed for several hours following the collision.
Anyone with information is asked to call 101, quoting incident number 577 of July 5.