The 46-year-old officer, named on social media as Dave Fields, 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.
Hundreds of people have paid tribute online to the pair and a fundraising page has been set up for their families.
Mr Fields was also a well-known football referee and was vice-chairman of Sheffield Referees Association.
A statement on the association's Facebook page said: "Dave wasn't just my best friend, he was vice chairman of Sheffield RA, the greatest mentor to referees, and especially to my kids. He was a referee, tutor and one of the good guys. Giving up his time to help anyone.
"Most of all he was a dad and husband and my thoughts are so so much with his family at such a difficult time.
"He loves football and loves his job as a police officer and his passing will leave a hole in so many lives."
Commenting on the association's post, Andy Hogg wrote: "Dave Fields - lover of football, lover of refereeing, lover of people, lover of life.
"He was not in the Premier League of top blokes, he was in the Champions League.
"TQ Fieldsey for your friendship, your loyalty, your kindness and most importantly, your wicked and wonderful sense of humour."
Clinton Cooper wrote: "Very saddened to hear this awful news. Thinking of Dave and his family and friends.
"My involvement with Sheffield Referees Association allowed me to meet and work with some wonderful people over many years. None finer than Dave.
"A really lively sense of fun and the most helpful friend to so many colleagues.
"Dave ran the line to me a number of times and took his active refereeing performances very seriously - again leading to the high esteem in which he was held.
"There are many friends, family and those in the wider community whose lives Dave has touched and enriched. I’ll miss Dave."
Trevor Sherwood, editor of Crime and Policing News Website, has set up an online fundraising page to raise money for both families.
He 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."
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.