Wayne Couzens has been given a whole life order for the kidnapping, rape and murder of York woman Sarah Everard.
It means he will never be released and will die in jail.
The officer strangled Ms Everard with his police belt after kidnapping her under the guise of a fake arrest for breaking lockdown rules.
Couzens, 48, stood with his head bowed throughout the sentencing hearing and did not look up as he was ordered by the judge to stand.
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He shook slightly as he was jailed in front of his victim’s family, who calmly looked on from the well of the court.
Sarah Everard’s parents Jeremy and Susan clasped hands and hugged police officers after Couzens shuffled out of the dock to be taken down to the cells.
Sentencing Couzens for the murder of Sarah Everard, Lord Justice Fulford said the circumstances of the case are “devastating, tragic and wholly brutal”.
The judge said Ms Everard was “a wholly blameless victim” of a “grotesque” series of offences which culminated in her death and disposal of her body.
The evidence gathered against Couzens was “unanswerable” and there was “no credible innocent explanation” for it, he said.
Couzens went “hunting a lone female to kidnap and rape” having planned in “unspeakably” grim detail, the judge said.
The defendant’s preparations included taking some of his police kit with him and lying to his family about working on the night of the murder, the Old Bailey heard.
Sarah Everard was brought up in York and went to Fulford School before going to university and settling in Brixton, south London.
The judge paid tribute to the dignity of Ms Everard’s family, whose statements in court revealed the human impact of the “warped, selfish and brutal offending which was both sexual and homicidal.”
Lord Justice Fulford said Couzens tried to “minimise his true responsibility” for what had occurred from the moment he spoke to police.
He said the defendant must have realised he “may well need to kill the woman he intended to abduct and rape” but that did not become a “definite outcome” before events began to unfold.
How Couzens was arrested
The court had heard how Couzens used his Metropolitan Police-issue warrant card and handcuffs to snatch Ms Everard as she walked home from a friend’s house in Clapham, south London, on the evening of March 3.
The firearms officer, who had clocked off from a 12-hour shift at the American embassy that morning, drove to a secluded rural area near Dover in Kent, where he parked up and raped Ms Everard.
Ms Everard, who lived in Brixton, south London, had been strangled with Couzens’ police issue belt by 2.30am the following morning.
Married Couzens then burned her body in a refrigerator in an area of woodland he owned in Hoads Wood, near Ashford, before dumping the remains in a nearby pond.
He was arrested at his home in Deal, Kent, after police connected him to a hire car he used to abduct Ms Everard, whose remains were found by police dogs on March 10.
Police waited for two hours before moving in to detain the officer, giving him the chance to wipe his mobile phone beforehand.
In an emergency interview at his home, Couzens concocted a fake story that he had been “leant” on by a gang which forced him to hand over “a girl”.
He went on to plead guilty to Ms Everard’s kidnap, rape and murder and was sacked from the force in July.
On Wednesday, Ms Everard’s parents Jeremy and Susan and sister Katie asked Couzens to look at them, condemning him as a “monster” as he sat quaking in the dock with his head bowed.