The 103 children - almost all of whom are from Chad - have been staying at a Unicef orphanage in Chad's capital, N'Djamena, in the wake of the scandal involving the Zoe's Ark charity, which claimed that they were Darfur refugees.
The 21 girls and 82 boys aged between one and 10 years will be handed over to relatives in Chad "in the coming days", Veronique Taveau, Unicef spokeswoman, said.
Earlier, Unicef had linked the time it was taking to return the children to their families to bureaucracy, Chadian government's determination to ensure the children were returned to the correct guardians and insecurity in eastern Chad.
Part of the problem was that Zoe's Ark, the little known French aid group involved, had left little paperwork identifying the children, Unicef officials had said.
Zoe's Ark had said it intended to fly the children - whom it identified as war orphans from neighbouring Sudan's wartorn Darfur province - to France, where they were to be cared for by host families.
But investigations showed the children were Chadian, not Sudanese, and that most of them had at least one parent or close adult relative.
Last December, the charity's head Eric Breteau and five colleagues were sentenced to eight years hard labour by a Chad court for the attempted airlift.
Days later, they were sent to France under a judicial agreement between the two countries.
In France, which does not have a hard labour sentence, their sentences were converted into eight years in prison.
Chadians were so angered by the affair that they staged a stone-throwing, anti-French demonstration in the capital, N'Djamena.
The case raised tensions between France and Chad, a former French colony.
Idriss Deby, Chad's president who has received key support from the French government in the face of attacks by Chadian rebels, said he was considering pardoning the aid workers, but wanted the children's families to receive some $12.26 million in compensation.