The man, 36, is due to land at the Landvetter airport and will be taken into custody in Uddevalla. He will be questioned on Thursday, according to the prosecutor.
"We will see what consequences this will have for the investigation, but it is, of course, good to be able to talk to the suspect. It is a step in the right direction," prosecutor Per-Erik Rinsell told Swedish Radio's P4 Väst station.
The suspect was arrested by Polish police when he walked into the Swedish embassy in Warsaw, around two weeks ago.
His lawyer, Tommy Nilsson, has not been in contact with him since then.
The man is suspected of killing the woman, 23, who disappeared from her home in Trollhättan some six weeks ago. Police found large amounts of blood in her apartment. After searching for five weeks, they found her body in a wooded area outside Grästorp last Thursday.
Two other men, aged 31 and 35, have been detained on suspicion of protecting a criminal and of serious crime.
All three suspects deny the accusations.