Ms Everard, 33, a marketing executive who is originally from York, was killed in March after disappearing while walking home in Clapham, South London.
She was reported missing by her boyfriend on March 4 and her body was found hidden in an area of woodland in Ashford, Kent, on March 10.
Pc Wayne Couzens, of the London force, pleaded guilty to the kidnap and rape of Ms Everard at the Old Bailey this morning (Tuesday).
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 while medical reports are ongoing.
The Metropolitan Police officer was wearing khaki trousers and a grey sweatshirt as he appeared by video link from Belmarsh jail.
He pleaded guilty to kidnapping Ms Everard “unlawfully and by force or fraud” on March 3.
He also pleaded guilty to a second charge of rape between March 2 and 10.
Couzens was not asked to enter a plea to her murder between March 2 and 10.
The defendant said: “Guilty, sir” when asked for his plea to the first two charges.
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 July 9.
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