The mother of Cleo Smith has declared her “family is whole again”, after her four-year-old daughter was found alive and well more than two weeks after she went missing from a campsite in remote Western Australia.

Western Australia police said they had found Cleo alone in a house in Carnarvon, about 900km north of Perth, at 1am on Wednesday. They arrested a man a short time later.

The WA police commissioner, Chris Dawson, told the ABC that police had a 36-year-old man in custody. He said there was “no family connection”.

The house she was found in was declared a forensic scene with police officers combing through it, looking for extra evidence that will help piece together how she was taken.

“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,” Dawson said. “The fact she’s been found alive … I think Australia is rejoicing, you know, it is such a wonderful outcome.”

Dawson said the community in WA, and particularly in Carnarvon, deserved credit for helping with the investigation after police received information about a car connected to her disappearance.

Cleo’s mother, Ellie Smith, posted on Instagram at about 6am local time about her daughter’s discovery with the caption “our family is whole again”.

The police deputy commissioner, Col Blanch, said police had broken into the locked house and found the girl in one of the rooms.

“It’s my privilege to announce that in the early hours of this morning, the Western Australia police force rescued Cleo Smith,” he said.

“Cleo is alive and well. One of the officers picked her up into his arms and asked her, ‘What’s your name?’ She said, ‘My name is Cleo’.”

Cleo was reunited with her parents a short time later.

The four-year-old vanished from the Blowholes campsite near Carnarvon on 16 October.

Her mother was the last known person to see her. Smith said her daughter had woken up about 1.30am asking for water before going back to bed. In the morning Cleo and her sleeping bag were gone from the family’s tent.

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

The Carnarvon shire president, Eddie Smith, told 2GB radio he had realised something was going on when his phone started ringing on Wednesday.

“My phone started to ring flat out and I knew there was something going on here,” he said. “Cleo Smith had been found. I rang the police and they told me it was correct.”

Australia’s leaders were quick to express their joy at the news and to thank the police and others who had searched for Cleo over two harrowing weeks.

The prime minister, Scott Morrison, called Cleo’s discovery “wonderful, relieving news”.

“The fact that that nightmare has come to an end and our worst fears were not realised, is just a huge relief and a moment for great joy,” Morrison said during a press conference in Dubai on Wednesday.

Morrison said Cleo’s disappearance had “captured the hearts of Australians as we felt such terrible sorrow for the family”.

“I want to thank, particularly, all of the police and all of those who were involved in making sure that Cleo is safe and we are so thankful…I just thank God that Cleo is home and that she is safe,” Morrison said.

The Labor leader, Anthony Albanese, said it was “such happy news”. “To all those who tirelessly searched for this little girl, you deserve our thanks.”

Blanch said the outcome was down to “some incredible police work”.

“I want to thank Cleo’s parents, the Western Australian community and the many volunteers. And of course, I want to thank my colleagues in the Western Australia police force.”

The NSW police commissioner, Mick Fuller, told 2GB his WA counterpart, Dawson, told him he had broken down and cried at the news.

Fuller said he had thought the chances of finding Cleo alive were “so slim”.

“West Australian police never gave up on Cleo: it was good old-fashioned police work that resulted in her being found alive,” Fuller said.

Blanch said the man in custody was being questioned by detectives.

“We’ll have more to say on the rescue of Cleo as the day unfolds,” Blanch said. “For now – welcome home Cleo.”

A press conference was expected to be held mid-morning Perth time.

Det Insp Jon Rouse, the manager of victim identification at the Australian Centre to Counter Child Exploitation, said he had emailed colleagues in WA early on Wednesday morning to congratulate them. Rouse said he had seen the heartbreak when children could not be recovered, including the tragic case of the Queensland boy Daniel Morcombe, who was abducted from a bus stop in 2003.

A taskforce of 100 police officers, led by Det Supt Rod Wilde, had been based out of Carnarvon for 18 days looking for clues into Cleo’s disappearance. They used reconnaissance planes to carry out real-time surveillance.

The position of the zipper on the tent flap – too high for Cleo to reach – suggested she had not opened the tent herself.

“The positioning of that zipper for the flap is one of the circumstances that has caused us to have grave concerns for Cleo’s safety,” Insp John Munday said five days into the search.

That prompted police to pursue the “nightmare scenario” that she had been abducted.

Cleo’s mother maintained throughout the ordeal that Cleo would never have left the tent on her own.