Rescuers found the 14-year-old boy and the 12-year-old girl in bushland in the state's central west after the pair were reported missing.
They had spent almost 24 hours lost in bushland around Kains Flat, about 35 kilometres northeast of Mudgee.
Emergency services were called after they went for a walk at around 2.30pm on Monday and didn't return.
Following an extensive search involving police dogs, paramedics, Rural Fire Service volunteers and rescue helicopters, the children were spotted by the chopper at about midday on Tuesday.
A critical care paramedic was winched down from the chopper and assessed the children for minor abrasions before they were reunited with their parents.
The family extended their deepest thanks and gratitude to volunteers and the community for helping find their missing children.
"Our family would like to give our deepest thanks to emergency services and volunteers for assisting in the safe recovery of our children," a statement from the family read.
"We also extend a special thank you to the community from both Mudgee and Sydney."
Critical care paramedics and doctors as well as eight paramedic road crews took part in the search and rescue over two days.
Inspector Jed Gollan from NSW Ambulance said the children were doing well.
"When our critical care paramedic reached them, the children were tired, thirsty, and had quite a few mosquito bites but they were otherwise in good health," Inspector Gollan said.
"Reuniting them with their parents was a great moment."
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