His lawyer earlier said Rakhat Aliyev, a former ambassador to Austria, would hand himself in to Austrian authorities and wanted to cooperate with their enquiries, the APA press agency reported.
The case has been an issue in Austria for years.
A court in the central Asian republic of Kazakhstan found him guilty of the murder of two bankers who were kidnapped in 2007 and found dead in 2011.
Austria twice refused to extradite him, believing he would not receive a fair trial back home.
In July 2011, Austrian justice launched its own enquiry against Aliyev, who had since left for Malta.
Aliev, a politician and businessman, claims to be the victim of political intrigue after expressing ambitions to stand for the Kazakh presidency.
He was formerly married to Dariga Nazarbayeva, eldest daughter of Kazakh strongman Nazarbayev.
Last month she was elected as deputy speaker of the Mazhilis lower house of parliament and leader of the parliamentary faction of the majority Nur Otan party.
Long seen as a potential successor to her father, she had disappeared from public view when her former husband fell out with Nazarbayev, only returning to politics in 2012 when she was elected as an MP.
Nazarbayev, 73, has ruled Kazakhstan for two decades, making the energy-rich state into a magnet for foreign investors, but he is often criticised for jailing his critics and shutting down dissenting media.