Police motorcyclist PC Matt Lannie, aged 40, died when his bike was involved in a collision with a Toyota Avensis on Nether Lane, Ecclesfield, on Tuesday afternoon.
An investigation into the collision is under way but PC Lannie was on-duty at the time and responding to reports of a silver BMW failing to stop for officers.
He was pronounced dead a short time after the crash.
Superintendent Paul McCurry has paid tribute to the officer on Twitter.
He said: “It has been a difficult couple of days following the tragic death of a much-loved member of the South Yorkshire Police ‘Operations’ family.
“PC Matt Lannie was a dedicated officer and fantastic character.
“It was a privilege to have him as part of our team. We will all miss him.”
Posting on Facebook, Martin Judge described PC Lannie as ‘a true hero’ and Sarah Goodison Hardwick said he was a ‘brave man doing a job that is dangerous’.
Yesterday, Chief Constable Stephen Watson said: “Dreadful events such as these serve to remind us of the great dangers that police officers confront every day in order to keep us all safe.
“Matt was a specialist motorcycle officer in our roads policing unit and prior to this was a response officer at Sheffield.
“He was a very popular member of the team and he will be greatly missed.”
Any witnesses to the collision should call 101 and quote incident number 374 of April 21.