“I am delighted the suspect sought by justice is back in Germany,” said Interior Minister Horst Seehofer in a statement, adding he hoped Ali Bashar, 20, would now “rapidly” face trial.
Bashar is alleged to have strangled 14-year-old Susanna Maria Feldman after raping her in the German city of Wiesbaden.
He was detained in northern Iraq on Friday following an outcry in Germany after police hunting the fugitive admitted he had fled with his family.
Despite the absence of a formal extradition treaty between Iraq and Germany, he was put on a Lufthansa flight to Germany from the Kurdish regional capital Arbil, German media reports said.
He was expected to face a remand hearing after landing in Frankfurt and being transferred by helicopter to the police prefecture at nearby Wiesbaden, police said.
Bild daily said German police chief Dieter Romann, who has developed close relations with the Iraqi authorities, had personally travelled to Arbil to facilitate the handover.
The case has put renewed pressure on Chancellor Angela Merkel's government over the decision to open Germany's borders at the height of Europe's refugee crisis in 2015, resulting in the arrival of more than a million asylum seekers.
Demonstrators held a minute's silence in cities across Germany on Saturday, notably in the teenager's hometown of Mainz.
On Friday, a senior official in the autonomous Kurdistan region had told AFP that authorities were working to transfer Bashar quickly back to Germany to face trial.
“During interrogation following his arrest, the young man originally from Kurdistan confessed to killing the German girl,” said Tariq Ahmad, police chief for the Dohuk province of Iraqi Kurdistan.
“He said that the two of them were friends but that they had a dispute, and that he killed her when the girl threatened to call the police,” Ahmad said.
Bashar arrived in Germany in 2015 along with his parents and five siblings. He should have been deported after his request for asylum was rejected in December 2016, but he obtained a temporary residence permit pending his appeal.
During this time, he got into trouble with the police on several occasions, including for fights, alleged robbery and possession of an illegal switchblade.
He was also among the suspects for the sexual assault of an 11-year-old girl living in the same refugee shelter.
Seehofer said Bashar's return was but “small consolation” for the victim's parents who he said were in his thoughts.
“For the state of our society it is important these crimes be cleared up and that the suspects be brought to justice,” he added.