The children's father and one of their sisters, too, are in hospital with symptoms of bird flu.
Hariadi Wibisono, a Health Ministry official, said they were awaiting the result of tests on blood and swab samples from them at a World Health Organisation lab in Hong Kong.
The 4-year-old boy and his 13-year-old sister died last week, but confirmation only came back from the Hong Kong lab on Saturday, said Wibisono.
Meanwhile, their father and the sister were in stable condition and local tests showed them negative of bird flu, he said.
Like most of Indonesia's other cases, the victims lived on Java, a densely populated island home to more than half of the country's 220 million people.
Health experts watch such cases, known as "clusters", closely to see if there is evidence that the virus is passing between humans.
Officials have said there is no evidence of human-to-human transmission of the virus in Indonesia.
Bird flu has killed hundreds of millions of chickens and ducks since it started ravaging poultry stocks across Asia in 2003.
At present, the virus is thought to have only a limited ability to jump from poultry to people, but experts worry it might mutate into a much more virulent strain.
The human toll from the virus now stands at least 81 people in east Asia and Turkey since 2003.
Almost all the deaths have been linked to contact with infected poultry.