The children's father and one of their sisters are also in hospital with symptoms of bird flu, but tests on blood and swab samples from them have not been completed at the WHO-sanctioned lab in Hong Kong, said Health Ministry official Hariadi Wibisono.
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.
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.
The deaths were the fifth time members of the same family or close neighbors had contracted bird flu at the same time in Indonesia. Health experts watch such cases, known as "clusters", closely to see if there is evidence that virus is passing between humans.
Officials have said there is no evidence of human-to-human transmission of the virus in Indonesia.
The deaths bring to 14 the number of people killed from the disease in Indonesia.
Bird flu has killed hundreds of millions of chickens and ducks since it started ravaging poultry stocks across Asia in 2003.
The virus has a limited ability to jump from poultry to people.
The human toll from the virus now stands at at least 81 people in east Asia and Turkey since 2003.
Almost all the deaths have been linked to contact with infected poultry.