PC Wayne Couzens, 48, previously admitted rape and kidnap at the Old Bailey.
The police watchdog has also announced it is examining allegations that police failed to investigate indecent exposure allegations against him in 2015.
Couzens was due to stand trial on the charge of murder but pleaded guilty at a hearing on Friday.
His defence barrister, James Sturman QC, told the court: “His pleas represent truly genuine guilt and remorse for what he did and as he put it to us this morning, he will bear this burden for the rest of his life and he deserves to. Those are his words.”
In initial police interviews, Couzens falsely claimed that he kidnapped Ms Everard after being threatened by an Eastern European gang, and handed her over to them alive and uninjured.
Lord Justice Fulford remanded him in custody at HMP Belmarsh ahead of a two-day sentencing hearing starting on 29 September.
Carolyn Oakley, of the Crown Prosecution Service, said: “We still do not know what drove him to commit this appalling crime against a stranger. “
Couzens is separately suspected of indecent exposure in an incident on 28 February, days before the murder.
The Independent Office for Police Conduct (IOPC) is investigating whether the Metropolitan Police responded appropriately to the incident at a fast food restaurant in south London.
It is among five investigations linked to the killing and Couzens’s previous conduct, including another alleged indecent exposure incident in 2015.
Scotland Yard said it stopped paying Couzens following his initial guilty pleas to kidnap and rape, which was “as soon as legally possible”, and would formally dismiss him at an upcoming internal hearing.
Commissioner Cressida Dick said she had apologised to Ms Everard’s family and added: “All of us in the Met are sickened, angered and devastated by this man’s truly dreadful crimes. Everyone in policing feels betrayed.”
Ms Everard, a 33-year-old marketing executive, was abducted as she walked home from a friend’s house in Clapham on 3 March.
The Metropolitan Police launched a search after her boyfriend reported her missing the following day.
Ms Everard’s disappearance sparked a resurgence in demands for action on the safety of women and girls, including a vigil on Clapham Common.
Couzens was arrested at his home in Deal, Kent, on 9 March but had wiped his phone minutes earlier.
Ms Everard’s body was found in woodland near land owned by Couzens in Ashford, Kent, the following day.
The court heard that Couzens had not previously met Ms Everard and there was no previous contact between the “total strangers”.
Couzens, who joined the Metropolitan Police in 2018, had booked the hire of a Vauxhall Astra and bought a roll of self-adhesive film days before the murder.
At around 9pm on 3 March, Ms Everard set off on foot for the two-and-a-half-mile journey home, chatting with her boyfriend on the phone as she walked.
A camera attached to a passing marked police car captured her walking alone at 9.32pm.
Just three minutes later, a bus camera appeared to capture the moment she was intercepted by Couzens in Balham, south London.
Two figures could be seen standing by the hire car, which was parked on the pavement with its hazard lights flashing.
After abducting Ms Everard, Couzens drove out of London, arriving in the area of Tilmanstone, near Deal, at 1am.
Investigators tracked the route of the car using CCTV and ANPR cameras and identified the driver as a serving officer through the car hire firm.
Couzens had used his personal details and bank card to make the booking, picking up the Vauxhall Astra on the afternoon of the abduction and returning it the next morning.
In the days that followed, Couzens reported that he was suffering from stress and did not want to carry a gun any more, according to a case summary.
On 8 March, he did not report for duty and reported himself as being ill.
The next day, police arrested Couzens at 7.50pm – 39 minutes after he wiped the data from his mobile phone.
In an official interview, Couzens concocted an elaborate false story and claimed to be having financial problems after paying for sex in Folkestone.
He said he had got into trouble with a gang of Eastern Europeans who threatened him and his family.
A gang demanded he deliver “another girl” after underpaying a prostitute a few weeks before, he said.
He told investigators he kidnapped Ms Everard but then handed her over to three Eastern European men in a van in a layby in Kent, alive and uninjured.
However, police found out that Couzens and his wife had bought a small patch of woodland in 2019 in Ashford.
Phone data led officers to the site and at 4.45pm a body was found some 100 metres outside the property boundary.
Even though Couzens’s phone had been wiped, cell site data linked him to the abduction and the area where Ms Everard was found in the early hours of 4 March and the days leading up to his arrest.
Following the discovery of the body, he made no comment in police interviews before being charged on 12 March.
In a tribute to Ms Everard, her family described her as “bright and beautiful – a wonderful daughter and sister”.
“She was kind and thoughtful, caring and dependable,” they added. ”She always put others first and had the most amazing sense of humour. She was strong and principled and a shining example to us all.
“We are very proud of her and she brought so much joy to our lives.”
Additional reporting by PA