Cleo was discovered by WA police officers about 1 am on Wednesday, alone in a room in the house in Carnarvon, some 75 kilometres south from where she went missing.

“One of the officers picked her up into his arms and asked her ‘What’s your name?’” Deputy Commissioner Col Blanch revealed.

“She said – ‘My name is Cleo.’”

A 36-year-old man from Carnarvon is in custody and is being questioned in relation to the suspected abduction.

Police say he has no connection to Cleo’s family and was not present at the house when Cleo was found.

The girl has been reunited with her mother Ellie Smith and Ms Smith’s partner Jake Gliddon. She is receiving medical care but is said to be in good physical health.

“Our family is whole again,” Ms Smith posted on Instagram alongside a photo of Cleo.

Blanch thanked the WA community, volunteers and officers involved in the 18-day search for Cleo.

He described seeing seasoned detectives “openly crying with relief”, saying it was the result of some incredible police work.

“We were literally looking for a needle in a haystack and we found it,” he told Perth radio 6PR.

“When she said ‘my name is Cleo’, I don’t think there was a dry eye in the house.

“This really did hit the heart of Western Australians, it went international and to see Cleo rescued this morning, I’m speechless.”

The state government had offered a $1 million reward for information to find Cleo but Blanch said it was not expected to be claimed.

He said police had received intelligence on Tuesday guiding them to the house but the breakthrough had been the result of investigators piecing evidence together.

“There were lots of things. There were car movements, there were phone movements, there were antecedents of people,” he said.

Talkback radio lines were flooded on Wednesday with callers describing their own emotion at learning the news.

Carnarvon Shire President Eddie Jones said the local community would be “elated, thankful” as they heard the good news.

“It is wonderful,” he told 6PR.

Premier Mark McGowan thanked police for their “incredible work” to bring Cleo home.

“I’m beyond relieved. The nightmare is now finally over for Cleo and her family,” he posted on Facebook.

Cleo vanished from a tent at the Blowholes campsite, about 950km north of Perth, after the family arrived on October 16.

She was last seen by her mother around 1.30am that night.

The search for Cleo captured national attention, including in NSW where the state’s police commissioner on Wednesday recounted a conversation he had with WA counterpart Chris Dawson after Cleo was found.

“He said when he got the call this morning he broke down and cried,” Mick Fuller told Sydney radio 2GB.

“It’s such an amazing story.”

Dawson, who will travel to Carnarvon on Wednesday, said it was one of the greatest moments in the history of the force.

“To find a little girl, a vulnerable little girl, after 18 days. Obviously, people think the worst. But importantly, hope was never lost,” he said.

“I think Australia is rejoicing. It is such a wonderful outcome.”

Dawson said that while police never gave up hope of finding Cleo, the longer the search went on the tougher it became.

“Having been around the block a bit, we obviously were very, very concerned [after] so many days passed,” he said.

WA investigators spoke to more than 110 people who were at the campsite when Cleo went missing.

They sifted through more than 1000 calls to Crime Stoppers and trawled through vast amounts of materials for forensic clues.

They had also been searching for the driver of a car seen leaving in the campsite in the middle of the night before it was discovered the child was missing.

WA Police had suspected she was abducted by an “opportunistic” offender. A press conference will be held later on Wednesday.

Prime Minister Scott Morrison said Cleo’s discovery was “wonderful, relieving news” and thanked police for their efforts.