Police footage of Cleo’s rescue showed her “smiling” and “as well as we could expect in the circumstances”, said Commissioner Chris Dawson, who added she was receiving medical care.
Authorities say the man in custody has no connection to the Smith family. No charges have been laid.
The house where Cleo was found is about six minutes’ drive from her family home in Carnarvon, which has about 5,000 residents.
ABC News reported a man who lived at the house had been recently spotted by a neighbour buying nappies.
“We didn’t click who… he was buying them for,” the neighbour was quoted as saying.
Deputy Commissioner Blanch said they scoured thousands of pieces of information looking for a “needle in a haystack”.
“Late last night they found that needle that led them to that address and rescued Cleo,” he told Network Seven.
Police said it involved information about a car, but would not elaborate.
Australian PM Scott Morrison tweeted it was “wonderful, relieving news”. Commissioner Dawson said: “I think Australia is rejoicing.”
“To find a little girl – a vulnerable little girl – after 18 days. You know, obviously people think the worst, but importantly hope was never lost,” the commissioner added.