They will appear at Westminster Magistrates’ Court on 16 March.
The Independent Office for Police Conduct (IOPC) has said that the charges relate to the case of Wayne Couzens, who murdered Sarah Everard.
The offences are alleged to have occurred between April and August 2019.
In a statement, the IOPC said: “The IOPC’s investigation began following a referral from the Metropolitan Police Service in April last year and was completed in December when we referred a file of evidence to the Crown Prosecution Service (CPS).
“The CPS has now taken the decision to authorise charges against the officers.”
Rosemary Ainslie, head of the CPS special crime division, said: “Each of the three defendants has been charged with sending grossly offensive messages on a public communications network. The alleged offences took place on a WhatsApp group chat.
She said the function of CPS was not to decide a person’s guilt but to make fair assessments about whether it was appropriate for a court to consider charges and added that nothing should be published that could jeopardise the defendants’ right to a fair trial.
In a statement, the Met said: “We are aware of charges brought against two serving Metropolitan Police officers and one former officer about sending grossly offensive messages on a public communications network.