The 46-year-old officer was responding to a call when the police car he was driving and another vehicle travelling in the opposite direction collided on the A57 near Shirebrook Valley Nature Reserve at around 8.15pm.
He was pronounced dead shortly afterwards and a 61-year-old Sheffield woman who was a passenger in the other car died in hospital. A 63-year-old man who was driving the other vehicle was also taken to hospital, where he remained today in a serious condition.
An online fundraising page has been set up to raise £1,000 for the families of the office and the woman.
Trevor Sherwood, editor of Crime and Policing News Website, who set up the page, said "Please help and support the family of these victims.
"This is a very tragic incident that has happened on Christmas Day.
"We have lost a member of the thin blue line and tragically a member of the public also.
"A police officer should never have to leave his family on Christmas Day knowing he'll never return"
"My thoughts are with both families and those officers, paramedics and fire crews who attended his tragic incident.
"Let's raise as much as we can in the memory of these fallen victims."
Hundreds of people have paid tribute online, and South Yorkshire Police has changed its Facebook profile to a thin blue line on a black background as a mark of respect, with others following suit in a show of solidarity.
Assistant Chief Constable David Hartley said: “On behalf of the force I’d like to offer my sincere condolences to all of those left bereaved by this terrible tragedy, our thoughts, love and support are extended to all those affected.
"We are doing everything we can to support them through this difficult time. I ask that their privacy is respected at this sad time.
“We have lost a friend and a colleague from our police family in this incident.
"The officer has been with us for 12 years and was a passionate, professional and universally liked officer. His colleagues, and everyone across the force, are devastated by what has happened.
"Our thoughts are with both families who have lost loved ones during this incredibly difficult time."
The Independent Police Complaints Commission is investigating the circumstances after being notified of the tragedy.
It said the officer had been travelling alone in the BMW 3 Series police car towards Coisley Hill when his car and the silver Citroen C3 collided.
Any witnesses, including those who saw either vehicle before the collision, are asked to call police on 101, quoting incident number 691 of December 25.
To donate click here.