A four-year-old girl has been rescued “alive and well” more than three weeks after she was suspected to have been snatched from a tent during a family camping trip on Australia’s remote west coast, police said.

Officers found Cleo Smith in a house in the coastal town of Carnarvon and a man was taken into custody in an early morning raid, Western Australia Police Deputy Commissioner Col Blanch said.

She had disappeared with her sleeping bag from her family’s tent at the Blowholes Campground, 75 kilometres (47 miles) north of the family home in Carnarvon, a town of 5,000 people, on October 16.

“Cleo is alive and well,” Blanch said.

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

She was reunited with her mother Ellie Smith and stepfather Jake Gliddon soon after.

It is unclear whether a one million Australian dollar (£545,000) reward offered five days after her disappearance led police to her.

She disappeared between 1.30am and 6am on the second day of a camping trip with her parents and younger sister Isla.

The children had been in a compartment of the tent separate from the parents.

Police suspected she had been abducted because a zipper on a tent flap had been raised to a height that she could not have reached.

Forensic scientists had examined the exterior of the family home for evidence that a predator had stalked Cleo and attempted to break in.

The disappearance had captivated the nation.

Prime Minister Scott Morrison thanked police for finding Cleo and supporting her family.

“What wonderful, relieving news. Cleo Smith has been found and is home safe and sound,” Mr Morrison tweeted.

“Our prayers answered,” he added.