The 39-year-old woman was attacked and stabbed in the street on Friday afternoon.
Several people were around to witness the act, including the woman's two young children, who saw their mother killed.
Police believe that the act may have been prompted by a custody battle between the man and the woman.
The man had been convicted of assaulting her in November, a verdict he appealed.
He had been released while waiting for the new trial date. On Sunday he was arrested once more.
"The district court judged that he was unlikely to relapse into crime," said the man's lawyer Ulf Bjermer to local newspaper Sydsvenskan, as an explanation for why the man was set free after his conviction.
"This was exactly what we feared would happen," said Roger Carlström, one of the police officers who headed the investigation of the previous assault, in reaction to reports that the man had killed the woman.
During the original assault, which occurred in October 2011, the 45-year-old man apparently forced the woman down to the floor, and put hand cuffs on her.
The man admitted the assault, but claimed to have been hit by a blackout.
He appealed the November conviction, wanting to serve a suspended sentence and community service instead of jail time.
While waiting for the retrial, the court ordered the man released, judging that he wouldn't impede the investigation.
The woman received police protection, however, including an emergency telephone.
But those extra measures were apparently not enough to protect her on Friday when her ex-boyfriend confronted her on the street and fatally stabbed her.
"The lawyer said that since the man was forbidden from contacting her it wasn't necessary to keep him locked up. But that was completely wrong," Carlström told Sydsvenskan.
According to the newspaper, police had also received warnings about the 45-year-old from his neighbour.