The kidnapper, identified as Claude Dubois, was wearing an electronic tracking bracelet while serving a penalty for murdering his former girlfriend.
He was arrested on Tuesday afternoon after his car crashed following a police chase.
At a news conference on Wednesday morning officials said that Marie's body was found in a wood at around 3am following information provided to investigators by Dubois.
Police said the body was formally identified but that an autopsy was still under way.
Vaud police chief Jacques Antenen said investigators questioned Dubois, who told police where the woman was.
The man admitted to kidnapping Marie and using tape to hinder her movements, Antenen said.
But police still do not know how or where the woman was killed, he said.
Witnesses saw the man arrested by police taking Marie by force in his car on Monday night, near the Payerne golf course in the canton of Vaud, northeast of Lausanne.
The woman was a resident of Payerne, a town located close to the border of the canton of Fribourg.
Around 100 officers were searching for Marie on Tuesday after police discovered she was no longer with Dubois.
Police said Dubois was still under house arrest and wearing an electronic bracelet, while serving a jail term for abducting, raping and murdering his former girlfriend in 1998.
Dubois was convicted in 2000 and served the first 12 years of his sentence in prison.
Questions are already being asked whether this man should have been released from prison.
Vaud police chief Antenen told the press conference that Dubois removed the electronic bracelet after abducting Marie.
He said that questioning of the suspect was interrupted after he informed police where Marie could be found.
Dubois subsequently refused to respond to questions but further questioning was planned later on Wednesday, Antenen said.
"We need to understand how a sexual predator could find himself at large," Jacqueline de Quattro, security and environment minister for the canton of Vaud commented at the press conference.
Béatrice Métraux, the canton's interior minister, said the government was "shocked and overwhelmed" by the tragedy.
She said an investigation would be made to examine the circumstances of the case.