Northumbria Police said Dougal was suspended from his job and an employment hearing would be held in the future.
The crash happened on Denton Road in Scotswood on 19 May.
The court was told that Dougal was reacting to the Volvo's automatic number plate recognition system, which alerted him to a passing car - indicating it could potentially be linked to a crime.
He accelerated to catch up with the Renault Megane and struck Hayley when she stepped into the road.
Dougal said he had not wanted to alert the other driver to his presence by putting on his sirens or blue lights.
But the number plate recognition data was later found to be out of date - the Megane was being lawfully driven by a Czech national.
Hayley Adamson's aunt Elizabeth Broom: 'Hayley was a lovely bubbly girl'
At the time of the crash, the qualified advanced driver was travelling so fast he had effectively become a passenger in his own car and had surrendered "to physics", an expert witness told the jury.
Retired police inspector and police driving standards expert Gordon Robertson said he "could not imagine" a situation where Dougal should have accelerated to more than 90mph, without activating his blue lights or siren.
The court was shown footage from the in-car video camera, including the moment the teenager was hit by the car and flung out of shot.
Judge David Hodson said: "You will be remanded in custody and you must appreciate that the inevitable outcome of a conviction of an offence of this nature is an immediate sentence of custody."
He added: "I am sure everybody who has sat through this case will be acutely conscious of the grief there has been to the Adamson family."
Pc John Dougal is a qualified advanced driver
The jury of eight women and four men took an hour and a half to reach its unanimous verdict.
Dougal was remanded in custody to be sentenced on 1 May.
Temporary Assistant Chief Constable Jim Campbell said: "Northumbria Police fully accepts responsibility for the death of Hayley Adamson and I would like to sincerely apologise to Hayley's family. We all share in their sadness at this terrible loss of a young life.
"The public place their trust in police officers to make judgements and act in a way that does not put them at risk and on this occasion we failed."
Hayley was due to sit the first of her GCSE exams, in English, the day after she was killed.
Her friends began a fundraising campaign to pay for a memorial and launched a "Justice for Hayley" fund.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.