The crash happened at 8.15pm on Christmas Day as the officer was travelling on the A57 south-east of Sheffield.
He had been responding to another incident when his BMW 3 Series collided with a silver Citroen C3 heading the opposite way.
The 46-year-old officer, who had served in the force for 12 years, was pronounced dead shortly afterwards, along with a 61-year-old Sheffield woman who was a passenger in the Citroen, who died in hospital.
A 63-year-old man was driving the Citroen and has been taken to hospital in a serious condition, police said.
The police car had been travelling towards Coisley Hill, to the south-east of the city, at the time. The Independent Police Complaints Commission (IPCC) has been notified about the crash and is investigating the circumstances.
South Yorkshire Police 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.”
Witnesses to the collision, or who saw either of the vehicles before the incident, are asked to call 101 quoting incident number 691 of 25 December 2017.