Pc Wayne Couzens, 48, appeared at the Old Bailey where he pleaded guilty to the kidnap and rape of the 33-year-old marketing executive, who disappeared on 3 March as she walked home to Brixton, south-west London.
The court heard Couzens accepted responsibility for the killing of Ms Everard, but was not asked to enter a plea to a charge of murder.
Ms Everard was walking home from a friend's house around 9pm when she went missing.
She was reported missing by her boyfriend the following day.
Her body was found hidden in an area of woodland in Ashford, Kent, on 10 March.
It was identified via dental records.
During his video link appearance from Bellmarsh jail on Tuesday, the Metropolitan Police officer was wearing khaki trousers and a grey sweatshirt.
He pleaded guilty to kidnapping Ms Everard "unlawfully and by force or fraud" on 3 March.
He also pleaded guilty to a second charge of rape between 2 and 10 March.
Couzens was not asked to enter a plea to her murder.
The defendant said "guilty, sir" when asked for his plea to the first two charges.
Four members of Ms Everard's family were present at the court as PC Couzens, who had served as an armed police officer, entered his pleas.
The court heard that responsibility for the killing was admitted, but medical reports were awaited.
Members of Ms Everard's family sat in court to witness the defendant enter his pleas.
A further hearing before Lord Justice Fulford is due to take place on 9 July.
The family of Ms Everard previously described her as a "shining example to us all" and said she "brought so much joy to our lives".
Couzens, who joined the Met in 2018, was arrested at his home in Deal in Kent in March, first on suspicion of kidnap. The next day, while in police custody, he was arrested on suspicion of murder.
Last week, the results of a post mortem were made public, which showed Ms Everard died from compression of the neck.