Austria announced on Saturday that it was preparing to repatriate two sons of an Austrian ISIS group supporter after conditions for their release were met.
Foreign ministry spokesman Peter Guschelbauer told public broadcaster ORF's Oe1 radio that "there is a positive DNA test and so the children are clearly identified."
Their mother is believed to have died in Syria after she headed there in 2014.
Guschelbauer said there has also been an Austrian court decision on custody "and so the conditions for repatriation are fulfilled."
ORF reported that a court last week awarded custody to the grandparents of the boys, who are one-and-a-half and 3 years old.
It said they have been at the al-Hol camp in Syria, controlled by Kurdish forces, for the past few months.
Four German children fathered by ISIS militants were handed over to Germany by Syria's Kurdish-led administration Monday.
Germany Foreign Minister Heiko Maas said it was "very gratifying" that the four children were no longer in Syria.
"We will continue to work so further children can leave Syria. They are mainly small children and their accommodation there is anything but ideal," he said.
"In the end, they can't be held responsible for the actions of their parents," he added.
Syria's Kurds have spearheaded the US-backed fight against ISIS in Syria, and in March expelled the extremists from their last patch of territory in the war-torn country's far east.
Even as they fight remaining sleeper cells, thousands of alleged ISIS fighters and family members are being held in their custody.
These include hundreds of suspected foreign fighters in their jails, and thousands of their alleged family members in overcrowded camps.
Western countries have been largely reluctant to repatriate their nationals.
But France and Belgium have brought a handful of orphans home, while the United States last year repatriated a woman with her four children.
Kazakhstan, Uzbekistan and Kosovo have repatriated dozens of women and children.
A dozen children of alleged extremist fighters have been repatriated from Iraq to Germany since March.
