When detective Cameron Blaine broke his way into the room of the small house on the outskirts of the Western Australian town of Carnarvon, he was pretty certain the four-year-old girl inside was the one he had been searching for.

But he needed to be sure.

“I asked her what her name was. One of the guys jumped in front of me and picked her up and I just wanted to be absolutely sure … I wanted to be sure it was her,” Blaine said.

“I said: ‘What is your name?’ She didn’t answer, I asked three times and then she looked at me and said: ‘My name is Cleo.’ And that was it.”

That was how one of the biggest and most dramatic searches in Western Australian police history ended on Wednesday morning. It was a hunt that engaged a nation and garnered widespread international attention.

The search for little Cleo Smith had begun 18 days before – just hours after police say she was taken in the dead of the night from the family tent she was sleeping in at the Blowholes campsite, a 10-hour drive north of Perth.

During the next fortnight, an army of officers sifted through rubbish along 600km of highway, scoured unforgiving bushland, and combed through homes, industrial estates and CCTV footage. The search area – a 1,000km radius from the campsite – was enormous.

Trackers were brought in and drones were deployed, as well as specialist aircraft to search the vast areas.

But in the end, Cleo was found in her home town of Carnarvon, less than 100km away from the family tent from which she disappeared on 16 October.

For Cleo’s mother, Ellie Smith, and stepfather Jake Gliddon – who had used televised addresses to beg and plead for their little girl to come home – the agonising wait was over.

At a press conference held in Carnarvon on Wednesday afternoon, Blaine told how he broke the news to the couple after some of the “shock and elation” of finding Cleo had passed.

“We had always hoped for that outcome but were not prepared for it. It was absolutely fantastic,” he said. “To see her sitting there in the way that she was, it was incredible.

“I turned around and walked out of the house. Not long after that, we got into the car … we called Cleo’s parents and said, we’ve got someone here that wants to speak to you. It was a wonderful feeling.”

Blaine said things developed so quickly he didn’t have time to fully prepare Ellie and Jake, but Cleo was reunited with her parents in hospital in the early hours of Wednesday morning.

Once reunited with her family, the four-year-old exclaimed: “Mum”. There were “big hugs, kisses and lots of tears,” Blaine said.

Earlier, Smith had posted on Instagram about her daughter’s discovery with the caption “our family is whole again”.

“Can I say after seeing her a couple of times this morning, she’s a little Energizer bunny,” Blaine said.

“How she has that much energy, I wish I did, I am about ready to go to sleep. [She’s] a very sweet, energetic girl, very trusting and very open with us. It was certainly an honour to see that reunion and have a part in it.”

Needle in a haystack

Exactly what led to the breakthrough that has been hailed as one of the greatest moments in WA’s policing history has not been explained in detail.

Police had offered a $1m reward for information, but deputy police commissioner Col Blanch said there was no key piece that broke open the investigation so that reward won’t be claimed.

“It’s a collation of a lot of different things but what I can say is humans, good people, put information together. And that’s what I really want to put it down to,” he said.

“There were lots of things – there were car movements, there were phone movements, there were antecedents of people.

“The jigsaw fit the puzzle but it took really good intelligence analysts and detectives and specialists to look at all of that information, put it together, and go, you know what? That doesn’t seem right to me … and we’re gonna act on it.”

Blanch said a 36-year-old man taken into custody by police for questioning was not known to the family and was the only suspect in the case.

He said the final moments of his force’s long search played out long before dawn on Wednesday, just 7km from Cleo’s own home.

He said detectives broke down in tears at the news and that the footage of body cameras worn by the four officers – who smashed their way into the house – capturing Cleo quietly giving her name is burned into his memory for ever.

“This is the outcome we all hoped and prayed for,” Blanch said.

“Literally this was a needle in a data haystack, and our very, very good officers and investigators and analysis in that taskforce found that needle late last night, and as a result executed that search warrant … just incredible.”

Blanch also criticised social media users who pointed the finger at Cleo’s family without basis during the investigation. He said the breakthrough should send a strong message to people not to jump to conclusions on these cases.

Dr Paola Magni, a forensic scientist at Murdoch University, said finding a child alive so quickly was a rare outcome.

“We have, in the history of criminology, many cases about abduction and kids have been found 15 years later as adults. In this case, the two weeks is such a good outcome,” Magni said.

She said police would have used a mixture of traditional policing, digital evidence and profiling analysis.

Community gets behind search

While police admit that a car spotted at 3am turning toward Carnarvon off the road that leads from the campsite was a crucial piece of the puzzle, lead investigator Det Supt Rod Wilde said it was hard police grind that solved this case.

“It was a lot of hard work, it wasn’t any one particular thing. It was just the process that we go through in a major investigation, dotting those i’s and crossing those t’s,” Wilde said.

He said taskforce Rodia received more than 1,000 calls from the community, but the final piece of intelligence that led to the house raid where Cleo was found was only discovered on Tuesday.

“People worked basically without sleep from the first occurrence when this happened. They have been working here tirelessly, never gave up hope and got the result that we are all so grateful for.”

The WA premier, Mark McGowan, said he was sent a photograph of a smiling Cleo in a hospital bed just after she was found.

“It is remarkable, exciting, uplifting news that was a surprise I’m sure to all of us but some great police work by some great people,” McGowan said.

McGowan said he initially missed the early morning call because he was asleep but woke at 3am and spoke to the commissioner.

“I was talking to the commissioner and he was so excited, he was almost emotional about finding little Cleo.”

On Wednesday afternoon the police commissioner, Chris Dawson, touched down in Carnarvon, held up a picture of Cleo and declared it a wonderful day.

The picture was taken earlier on Wednesday when Cleo was in hospital where she had been taken for medical tests. She was later discharged.

“It is a really special day for Western Australia,” Dawson said. “I’m just the proudest police commissioner I think in the world at the moment.”

Later still on Wednesday, Cleo’s mother updated a Facebook post – made on 17 October, 24 hours after Cleo went missing – that called for people to help to find her little girl.

Ellie Smith wrote: “FINAL EDIT – HOME WITH HER FAMILY.”