The remains were found in Brighton near where Marten, 35, and Gordon, 48, were arrested on Wednesday.
The couple were reported missing on 5 January with the baby.
More than 200 officers were looking for the infant after the pair were detained following a tip off from a member of the public.
Barry Hughes, chief crown prosecutor for CPS London North, said: “The CPS has authorised the Metropolitan Police to charge Constance Marten and Mark Gordon with gross negligence manslaughter.
“Constance Marten, aged 35, and Mark Gordon, aged 48, have also been charged with concealing the birth of a child and perverting the course of justice.
“These charges arise from their arrest on Monday as a result of a lengthy police investigation to establish their whereabouts and that of their baby.”
The pair will appear in custody at Crawley Magistrates’ Court on Friday.
The baby “had been dead for several weeks” before it was discovered, Metropolitan Police said on Thursday afternoon.
The gender of the infant is still unknown and a post-mortem examination is yet to take place, Detective Superintendent Lewis Basford said.
“Based on the enquiries we’ve carried out so far, we believe, sadly, the baby had been dead for several weeks before they were found. It’s too early for us to provide a more specific date,” he said.
The investigation team is “truly devastated”, Mr Basford said, while adding the importance of giving them “time and space” to investigate.
The Metropolitan Police has referred the case to the Independent Office for Police Conduct because the baby died during a missing persons investigation it was leading.
The couple disappeared after abandoning their burning car on the M61 near Bolton.
They used taxis to first travel to Liverpool, then Harwich in Essex, and on to east London, before arriving in Sussex on January 8.
They avoided detection by making payments only in cash, hiding their faces on CCTV and often moving around at night or in the early hours of the morning.
Marten grew up at Crichel House, a Dorset estate, and her grandmother was a friend of Princess Margaret. She was a promising drama student when she met Gordon in 2016. Since then the couple had led an isolated life cut off from family and friends.
Marten’s estranged father Napier Marten is a former page to the late Queen.
He and her mother Virginie de Selliers made public pleas through the media. Police offered a £10,000 reward for information leading to the couple being found.