The man called the emergency services himself after the attack, telling them that he had killed her, according to a report in the Aftonbladet daily.
The emergency services received the call at around 7.30pm on Sunday evening and when the first police unit arrived at the residence in Tyresö they found the injured woman.
The woman was rushed to hospital where she was pronounced dead.
The man was reported to be waiting calmly by the apartment building and left with the police.
“We went directly to the location where he was arrested calmly,” said Alexandra Godlund at Nacka police.
Earlier on in the evening the man was reported to have been having a barbecue with his four children.
The children have meanwhile been taken into care.
“They have been taken into care by social services,” said Alexandra Godlund.
The police will keep the questioning of the suspect, who has confessed to stabbing his ex-wife.
According to Aftonbladet sources the man has a previous record of violence directed towards his former spouse.
Police currently have no motive for the attack.