He is due to appear at Westminster Magistrates’ Court on Saturday morning.
It comes as police said Couzens was taken to hospital for a second time in 48 hours on Friday for treatment to another head injury sustained in custody, before he was discharged and returned to a police station.
He was previously treated in hospital for a separate head wound on Thursday, also sustained in custody when he was alone in his cell.
Metropolitan Police Assistant Commissioner Nick Ephgrave confirmed the charge in a statement outside Scotland Yard on Friday night.
He said: “I would like at this stage to pay tribute to Sarah’s family for their fortitude and forbearance through what can only have been the most intensely difficult few days.
“Our thoughts remain with them as this matter progresses.”
Regarding the second head injury, a Met Police spokesman said Couzens was being “monitored by officers” when he sustained the wound.
A spokesman said: “The suspect was taken to a hospital for treatment to a head injury sustained while in custody in a cell on Friday.
“He was being monitored by officers and received immediate first aid. He was discharged the same day and returned to custody.”
The Met Police said Couzens joined the force two years ago in September 2018 when he worked for a response team covering the Bromley area, before moving to the Parliamentary and Diplomatic Protection Command in February last year.
Couzens was arrested on Tuesday in Kent with Commissioner Nick Ephgrave commenting at the time that the fact he is a serving police officer “is both shocking and deeply disturbing”.
Ms Everard is thought to have walked through Clapham Common towards her house in Brixton – a journey which should have taken around 50 minutes.
Scotland Yard confirmed on Friday afternoon that human remains found in an area of woodland in Ashford, Kent, two days earlier had been identified as Ms Everard.
Her death has prompted an outpouring of grief from the public, with many women and girls sharing stories online of experiencing violence by men.
People have vowed to attend a vigil at Clapham Common in honour of Ms Everard on Saturday evening, despite the Metropolitan Police warning the public they should “stay at home or find a lawful and safer way to express your views”.
Organisers of the event, titled Reclaim These Streets, are continuing talks with the police to work out how it could go ahead safely, while a planned event in Edinburgh will now take place virtually.
Scotland Yard is facing an investigation by the police watchdog into its handling of separate allegations of indecent exposure against Couzens, whose primary role was on uniformed patrol duties of diplomatic premises, mainly embassies.
He was alleged to have twice exposed himself at a south London fast food restaurant three days before Ms Everard went missing.
The Independent Office for Police Conduct is to probe whether two officers “responded appropriately” in their investigation.
A forensics team searched an area of land outside the back fence of the Couzens’ house in Deal, Kent, on Friday, while uniformed officers were posted at a derelict garage in Dover, which was run by his family.
Police said a woman in her 30s, who was arrested on Tuesday on suspicion of assisting an offender, had been released on bail to return to a police station on a date in mid-April.