The man has been interrogated by both Swedish and Norwegian police since Monday, when he was found sleeping in his car wearing bloodied clothes in a car park north of Växjö, central Sweden.
“Interrogations have been held with him and he does not object to the extradition,” said Robert Loeffel of the Kronoberg police to the TT news agency.
The man admitted to the murder and told police on Tuesday exactly where they could find the body, following their 24 hour search.
The pair’s son, who is 11 months old, has been handed over to social authorities in Växjö and will be also taken to Norway to be looked after by the deceased woman’s relatives.
The woman, who was 26, was found dead on Monday in an abandoned cottage in the woods in Grøn-kjaer, not far from the man’s house in Norway.
A neighbour who heard the pair fighting on Sunday morning recounted hearing screaming around 10am on Sunday.
“I thought at first it was an animal,” Arndis Gudmundsdottir told the Expressen newspaper.
According to Norwegian daily Dagbladet, the victim was a Russian native who had come to Norway to study, and was taking time off to raise the couple’s child.
Police have not disclosed any details about the cause of the woman’s death, but Norwegian police said that a forensic investigation is underway.
The motive behind the murder also remains unclear, although an Aftonbladet source has pointed to a child-custody dispute.
It remains unknown exactly when the extradition will take place.