The Swiss 44-year-old man admitted under questioning to strangling his wife at their home in Assens following an argument that got out of hand, Vaud cantonal police revealed on Wednesday.
Information provided by the man led investigators on Tuesday to the place where he buried her in the woods near their home, police said.
The process of formally identifying the body has begun.
The corpse was unearthed and transported to the CURML centre for legal medicine in Lausanne for identification and an autopsy ordered by the prosecutor’s office.
But police believe the man’s confession brings a conclusion to the mystery of the woman’s disappearance, first reported on October 28th.
Investigators launched a massive search for the woman, who left behind a three-month-old baby boy.
Police and civil protection officers scoured the region around the couple’s home using tracking dogs.
An army helicopter was brought in for an aerial search.
Police also released several photos of the slim blonde woman in a bid to gain information as to her whereabouts from the public.
After the initial search uncovered no leads, police last month launched a criminal investigation, which narrowed to one suspect — the woman’s husband.
A process is under way to detain him until his case can be heard in court.
Vaud’s youth protection service, meanwhile, has taken charge of the baby boy.