It was a few hours after siblings Eli and Hannah Jones set off for a bushwalk on Monday in central western New South Wales that their family became concerned.
The 14-year-old and 12-year-old from Sydney left their campsite at Kains Flat near Mudgee in the afternoon but failed to return by nightfall.
Detective Inspector Natalie Antaw said the pair had visited the area once before and were not overly familiar with the site.
"They went for a bushwalk to have a look at a rock that's not too far from the actual campsite property," Detective Inspector Antaw said.
They had not taken any water or food on their walk and had not indicated what time they would be back at the campsite.
As the search intensified on Tuesday morning, a rescue helicopter delivered the news that the family, friends and the search teams had been hoping for.
Paramedics were winched down to the children and walked them out to a waiting ambulance.
They had minor cuts and scratches.
"It's a sensational feeling, not only for the family and friends of the children but it's also fantastic for the emergency services, the local community and the community in Sydney where the children are from," Detective Inspector Antaw said.
Police said the children became disorientated and lost in the bush.
The terrain was steep, rocky and wooded, and light misty rain had fallen on Monday night, pushing the temperatures down to the mid-teens.
Police have praised the children's resilience after being missing for more than 20 hours.
"It's a fantastic result and it's wonderful to see them reunited with obviously very relieved family and friends," Detective Inspector Antaw said.
A statement by the family, read by Detective Inspector Antaw, expressed gratitude to everyone involved in the search.
"The family would like to give our deepest thanks to emergency services and volunteers for assisting in the safe recovery of our children.
"Special thank you to communities from both Mudgee and Sydney."
