Philippa Reynolds, 27, was on routine patrol with two other officers, who sustained non serious injuries in the collision on the Limavady Road in the early hours of Saturday morning.
The officers were in an unmarked police car attending an unrelated call when the incident happened at approximately 3.40am. Two men fled the scene in the direction of Ebrington.
The vehicle had been stolen 40 minutes before the crash in the Gobnascale area.
The arrested men, aged 23 and 25, are being questioned by police.
Chief Superintendent Stephen Cargin said it is believed Constable Reynolds was killed instantly.
The patrol car was turning a corner when the stolen silver Toyota Land Cruiser hit it side on. It was struck between the driver's door and the passenger's door, the G District commander explained.
"Unfortunately Constable Reynolds was the rear seat passenger so she took the full impact.
"We believe that she was probably killed instantly."
The commander said it could have been any vehicle turning the corner into the path of the 4x4.
"It could have been anyone, it could have been a family that was struck," he said.
She was a young 27-year-old officer, with just two years’ service, in the prime of her life, doing what she loved to do - and that was serving the community to the best of her ability.
Chief Supt Stephen Cargin
The senior PSNI officer described Constable Reynolds as beautiful, bubbly, friendly and one of the most enthusiastic officers he had ever worked with.
He added that she had taken a career change - giving up teaching to join the PSNI in 2011.
"Her colleagues are devastated, as I am as her commander, as we all are as a police service," he said.
Constable Reynolds was from the Greater Belfast area.
"She typified the officers who are on duty 24/7, despite the pressures the organisation has faced over the last number of weeks," Chief Supt Cargin said.
"She was out there keeping people safe, serving her community to the best of her ability, out there doing her best like her other colleagues."
The Police Ombudsman has been informed of the fatal crash.
PSNI Chief Constable Matt Baggott said it was "with great sadness" that he learned of the death.
"This is a personal tragedy for her family and also for the whole Police Service. She was out on duty, working to keep people safe, when she died. My thoughts and prayers are with her family at this time."
I and my colleagues will ensure that no stone remains unturned as we work to bring to justice those who perpetrated this crime.
PSNI Chief Constable Matt Baggott
First Minister Peter Robinson and deputy First Minister Martin McGuinness have expressed their sympathy and urged anyone with information to contact the police.
"This is devastating news and we want to extend our heartfelt sympathies to the Police Officer's family, friends and colleagues.
"We wish her two police officer colleagues a speedy and full recovery."
The statement continued: "Officers in the PSNI put their lives at risk on a daily basis to serve and protect our community and we are all truly grateful for their dedicated service.
"Those who commit a crime such as vehicle theft must realise their actions can have serious consequences. We urge anyone with information to go to the police."
NI Secretary of State Theresa Villiers said this was "a tragic waste of a young life in sad and reckless circumstances".
Stormont Justice Minister David Ford said his thoughts were with the policewoman's relatives and the injured officers.
"I was shocked to hear of this tragic incident which resulted in the death of a police constable who was carrying out her duties serving the community in the middle of the night," he said.
"My thoughts and prayers are with her family at this time.
"I also send my best wishes to the two officers injured in this incident for a speedy and full recovery. It is hard to imagine how they, and indeed the wider PSNI family, are feeling."
Mark Durkan, SDLP MP for Foyle, said the policewoman was "tragically killed in the line of duty whilst doing her job to protect the community."
"My sympathies go out to her family and friends at this very difficult time, as they struggle to come to terms with this tragic news. My thoughts are also with the wider police family, not least those who were on duty alongside her, who have lost both a friend and a colleague," Mr Durkan added.
The shock felt across the community will be matched with disgust that such criminal activity has led to this tragic death.
SDLP MP Mark Durkan
Ross Hussey, Ulster Unionist Policing Board Member, said: "This young woman's death in the line of duty serves to re-emphasise the dangers faced by the officers of the Police Service of Northern Ireland on a daily basis, as they put themselves in harm's way to protect the whole community."
"They deserve our full support," the West Tyrone MLA said.
Brian Rea, Chair of the Policing Board, said "los(ing) a colleague, out on patrol protecting the community, is a terrible blow to the PSNI".
"On behalf of the Policing Board I would like to offer deepest condolences to the family, friends and colleagues of this young woman," Mr Rea said.
"They will have received the terrible news this morning and will be devastated by this tragic event."
The Garda Commissioner, Martin Callinan, also extended his deepest sympathies on the death of the young police officer.
"Our thoughts and sympathies are with our friends in Northern Ireland as they mourn the loss of their colleague. We also wish a speedy recovery to the officers injured in the incident," he said.
The Limavady Road was closed for most of the day at its junction with Glendermott Road and Clooney Terrace.
Police have appealed for witnesses to contact them.
Chief Supt Cargin said: "I would like to appeal to anyone who has information and may have seen the silver land cruiser travelling between the Gobnascale and Limavady Road areas between 3am and 3.30am this morning, or if they saw the two people who fled the scene and ran off towards the Ebrington area.
"Anyone with any information, no matter how small, please call us. These were officers who were out serving their community and we want the community to help us and give us the vital information we need."
Anyone with any information is asked to contact Strand Road Police Station on 0845 600 8000 or contact the independent charity Crimestoppers anonymously on 0800 555 111.