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

West Australian Police Minister Paul Papalia said her discovery was not a result of a chance sighting or a tipoff but of “hard police grind” by the 140-strong team assigned to investigate Cleo’s abduction.

The key to her discovery was put down to methodical analysis of witness statements, hours of CCTV footage and mobile phone data to try and pinpoint her whereabouts.

WA Police Commissioner Chris Dawson said the whole nation was rejoicing in Cleo’s discovery.

“She alive, she’s safe and she’s back with mum and dad,” he said.

One of four police who rescued Cleo, detective senior sergeant Cameron Blaine, descxribed the little girl as the “energiser bunny”.

“We were talking to her and she was talking to us. What can I say, having seen her a of couple times this morning, she is a little energiser bunny,” he told reporters.

“How she has that much energy, I wish I did, I am about ready to go to sleep. Very sweet, energetic girl. Very trusting and very open with us. We all wanted to take turns holding her. It was a really good experience.”

Dawson would not give any details on the 36-year-old man in custody over her alleged abduction other than he was a Carnarvon local. He has previously said he had no connection with Cleo’s family and was not in the house when she was found.

Police believe no other person was involved in taking her, describing it as an opportunistic abduction.

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“One of the officers picked her up in 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.

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

Authorities have so far been tightlipped on the exact intelligence that led officers to the property just minutes from Cleo’s family home.

The girl has been reunited with her mother Ellie Smith and Ms Smith’s partner Jake Gliddon. She was taken to hospital on Wednesday to be examined but was said to be smiling and in good physical health.

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

Mr 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.”

Premier Mark McGowan said he had received a message from the police commissioner in the early hours of the morning, with a photo showing Cleo smiling in her hospital bed.

“It was a surprise, I’m sure to all of us, but the result of some great police work by some great people,” he told reporters.

“It often is a tragic outcome but this is great news and uplifting for the entire country.”

The state government had offered a $1 million reward for information to find Cleo but Mr 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.

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, with her rescue described by University of Newcastle criminologist Xanthe Mallet as a “once in a lifetime miracle”.

NSW Police Commissioner Mick Fuller 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,” he told Sydney radio 2GB.

“It’s such an amazing story.”

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 material for forensic clues.

They had also been searching for the driver of a car seen leaving the campsite in the middle of the night on October 16.

WA Police had suspected she was abducted by an “opportunistic” offender. A press conference was set to be held on Wednesday in Carnarvon, a popular tourist town on WA’s northwest coast known for its banana plantations.

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