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The man, earlier identified as John Walsh, is also believed to have badly wounded his daughter.
He is currently being questioned about the attack in Cowra, 155 miles west of Sydney.
Paramedics were called to a house and found three bodies, including the children, said New South Wales state Ambulance Service spokeswoman Fiona Kruit.
The children's mother, who was a police officer, was attacked as she returned to the house and fled to a neighbour's place bleeding from a deep gash in one side of her head.
She was flown to hospital in a serious condition, Ms Kruit said.
Cowra Mayor Bruce Miller said the children were aged seven and five, and their mother, Shelley Walsh, was a police officer who worked in a nearby town.
Officers had previously released photographs to allow the public to help find Walsh.
A police statement says he was arrested without incident 258 miles west of Cowra at a motel in the town of Hay.
He was not immediately charged.