Wayne Couzens, 48, a serving London officer who guarded diplomatic premises, had previously admitted rape and kidnap.
He abducted Everard, 33, into a car rental as she walked home from a friend's house in south London on March 3 and her body was later found in woodland around 50 miles (80 km) away in southeast England. A post-mortem last month concluded she had died as a results of compression of the neck.
Appearing by videolink from prison for a hearing at London's Old Bailey Court, Couzens, bearded and wearing a blue sweatshirt, sat together with his head bowed and said "guilty ma'am" when asked how he pleaded to the charge of murder.
Prosecutor Tom Little said the officer had never met Everard before kidnapping her from London's South Circular road and that they were "total strangers".
Judge Adrian Fulford said Couzens had previously only given a completely false account of events, an elaborate story involving an eastern European gang.
"This has been a mammoth investigation which has produced some very significant leads to terms of having the ability to know what happened", Fulford said.
London Metropolitan commissioner Cressida Dick, Britain's most senior officer, told reporters outside court she had personally apologised to Everard's family.
"All folks within the Met are sickened, angered and devastated by this man's crimes. they're dreadful", she said.
Everard's murder provoked outpourings of anger from women who have recounted their own experiences and fears of walking the streets on their own in the dark , prompting Prime Minister Boris Johnson to vow action including money for better street lighting.
Couzens' lawyer, James Sturman, said his client's pleas represented "truly genuine guilt and remorse for what he did".
"As he put it to us this morning he will bear this burden for the remainder of his life, and he deserves to - his words 'and I deserve to'. He accepts the victims during this case are the Everard family and friends, not him", Sturman told the court.
A two-day sentencing hearing, which can consider psychiatric reports, will begin on Sept. 29.
