Officers visited the property at Coonabarabran, in NSW's Central West, at 2pm on Monday, following reports of a concern for their welfare.
The boys, aged six and seven, were found dead.
A 66-year-old woman, who police said was known to the children, was arrested at the property.
The woman, reportedly the boys' grandmother, was taken to hospital for further assessment where she remains under police guard.
The deaths are being investigated under Strike Force Darnum, assisted by detectives from State Crime Command's Homicide Squad.
Premier Chris Minns described the discovery of the boys' bodies as heartbreaking.
"What has occurred is terrible and as a state we share in the community of Coonabarabran's grief at the loss of two young boys who had their entire futures ahead of them," he said."I can not begin to imagine the heartbreak their loved ones are currently feeling, including their family, friends, and teachers."
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