Pc Wayne Couzens, 48, has pleaded guilty at the Old Bailey to the kidnap and rape of Sarah Everard.
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.
A post-mortem found Sarah Everard died from compression of the neck.
Marketing executive Ms Everard, 33, went missing as she walked home from a friend’s house in Clapham, south London, on March 3.
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.
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.
