The 24-year-old suspect had been arrested in February by Swiss authorities in a centre for asylum seekers in the north-eastern town of Kreuzlingen, not far from the Austrian border.
An extradition ruling carried out by the Swiss Federal Office of Justice found that the requirements for the extradition had been fulfilled, although the decision is not yet final as the suspect has 30 days to request an appeal.
The suspect, named as Abdou I. and who is originally from Gambia, is accused of killing the 25-year-old Lauren M., an American student and au-pair who was found dead in her apartment in Vienna on January 26th, having been suffocated.
Lauren M., who had been living in Austria for several years and was a German language student, was reported missing by her employers after she failed to pick up their child from kindergarten.
Firemen then broke down the door to the flat, leading to the gruesome discovery.
Local media reported that the Abdou I., a failed asylum seeker who had lost his right to stay in Austria, had been living with her in the apartment.
He had disappeared after the discovery was made but was found a few days later in the Swiss asylum centre.