The man, the father of her young son, was arrested on Monday wearing blood-stained clothes and suspected of having kidnapped the woman and her child from their Norway home.
The woman was still missing at the time of his arrest but has since been found dead in the Notudden forest close to the man's home in Norway.
Police found the 11-month-old baby safe.
The woman was found near a road, according to Norwegian police, who said that the man in interrogation with Swedish officers admitted to having killed the woman and told them where he had dumped the body.
Police in Norway received a phone call on Sunday from a woman asking for help. The line was suddenly cut off but the call was traced to a flat in Bø, west of Oslo.
Officers issued a description of the man’s car and informed other Norwegian police districts, as well as the Swedish and Danish police.
According to Aftonbladet, a 45-year-old man was arrested in Växjö, southern Sweden. Norwegian police said his clothes were soiled with blood stains.
”The arrest was completely undramatic,” said the Norwegian prosecutor Jon H Borgen to newspaper Aftonbladet.
The Norwegian police told the paper that the man is a Swedish citizen living in Norway, while the woman and child are Russian citizens who lived just outside Oslo.
The 45-year-old was not previously known to Norwegian police. After he had confessed his guilt, the police concentrated their search to the area where he said he had left the woman's body and subsequently found her.
The man is wanted for murder and a request to have him extradited to Norway will be filed on Tuesday, according to Aftonbladet.