The surprising U-turn came after the siblings - 12-year-old Lili and her brother Howick, 13 - went into hiding ahead of their expected deportations on Saturday.
In a statement, the Dutch Ministry of Justice and Security said that while authorities in the Netherlands and Armenia had worked hard to arrange a secure situation for the pair in Armenia, "recent developments" meant "the welfare and security of the children can no longer be sufficiently guaranteed".
"The state secretary has therefore, taking everything into account, decided that the children can remain in the Netherlands," Saturday's statement added.
Going into hiding
Earlier on Saturday, Maarten Molenbeek, spokesperson for the justice ministry, said the children had run away from a foster home overnight, while police appealed for the public's help in locating them.
Police reported in the afternoon that the siblings had been found and were being questioned, but would be returned to foster care.
The children have been living with foster parents since their mother, Armina Hambartsjumian, lost a decade-long legal battle for asylum and was sent to Armenia without them.
It was not immediately clear whether Hambartsjumian, who was deported to Armenia last year, would be allowed to return to join her children.
The siblings, who came to the Netherlands in 2008, have reportedly never visited Armenia and do not speak Armenian.
A court in the Dutch capital, Amsterdam, rejected a final bid to block their deportations on Friday.
The Dutch government faced mounting disapproval of its original refusal to let the siblings remain in the country.
Mark Harbers, state secretary for justice and security defended the government's position on Friday but acknowledged it was a tough decision to deport them.
"Everybody feels emotional about this; that also applies to somebody in the cabinet like me," Harbers said.
"But at the same time, you have to keep looking at all the facts that play a role."