The man suspected of abducting a four-year-old Australian girl "acted alone", police said Thursday, as they released an audio recording of the touching moment she was rescued.  

Cleo Smith disappeared from her family's tent in remote Western Australia last month, sparking a frantic air, land and sea search.

She was missing for 18 days until being rescued in a night raid on an empty home in the coastal town of Carnarvon - just a short drive from where she went missing.

A 36-year-old man was arrested nearby and is expected to be charged later Thursday after sustaining unspecified injuries in custody and being treated in hospital.

Lead investigator, detective superintendent Rod Wilde said police will allege he "acted solely alone" in abducting the little girl.

"He's back at the police station now speaking to officers at the moment," Wilde told reporters.

Police did not reveal what specific charges he was facing.

Many had feared the search for Cleo Smith would end in tragedy, but the discovery of her "alive and well" sparked elation Down Under, with police admitting "seasoned detectives" were "openly crying with relief".

The force on Thursday released audio recording of the rescue, in which officers can be heard urgently trying to affirm her identity.

"We've got her", "you're alright" excited police are heard to say, before another asks "what's your name? what's your name? what's your name, sweetheart." 

"M-my name is Cleo" the girl eventually responds. "Your name is Cleo" the revealed detective repeats. "Hello Cleo."

After Cleo's ordeal was over her mother, Ellie, posted on Instagram that "our family is whole again".

Their small hometown of Carnarvon, which had spent weeks on edge after the girl's disappearance, was soon decked out in balloons and "welcome home" signs as residents celebrated the news.

One of her rescuers, detective Cameron Blaine, said he visited the family after Cleo was released from a brief hospital stay Wednesday and she appeared to be coping well.

"It was really heartwarming to see her interact and playing in the backyard and just being herself and around her parents," he said.

"I'm amazed she seems to be so well-adjusted and happy."

Cleo's mother had woken at 6 am on October 16 to find the family's tent unzipped and her oldest daughter missing, sparking a massive ground, air and sea search.

Police have said they believe the abduction was unplanned and "opportunistic".