He made his confession in police questioning, confirmed the officer leading the investigation, Lars Hamrén.
Police were called to the apartment on Brogatan in central Halmstad just before 9am on Monday. The woman, who had been stabbed, was already dead by the time the police arrived.
A short while later, a man in his 30s went into the police station just a few hundred metres from the crime scene. The man was covered in blood and was carrying a knife. His appearance matched that described by a witness.
At first he told police that he had ‘done something’ without explaining precisely what it was.
But the admission came during interrogation later in the day.
The 50 year old woman worked at a psychiatric clinic and the man in custody was a former patient.
On Monday evening it emerged that the woman had been threatened by the man for some time. He had been given a restraining order preventing him from visiting her, but that had expired.