Rajwinder Singh touched down in far north Queensland aboard a privately chartered jet on Thursday after spending his first night in Australia behind bars following his extradition from India.
Ms Cordingley's body was found by her father partially buried in the white sand of Wangetti Beach in October 2018.
Detective Inspector Sonia Smith says it's expected Mr Singh will be formally charged with her murder later on Thursday night.
The 38-year-old is expected to appear in Cairns Magistrates Court on Friday morning.
"The murder of Toyah had a significant impact on everybody and I acknowledge that her family and friends are still dealing with the loss," Det Insp Smith told reporters.
"Now that the matter is before the court, I'd ask that the community not speculate and allow the justice process to be undertaken."
Police refused to say if any additional charges would be laid on Mr Singh, or if he'd formally agreed to be interviewed upon his arrival at the Cairns watch house.
However, he's unlikely to be able to make any immediate bail application due to the seriousness of the murder charge.
Toyah's father Troy Cordingley said it was "a very difficult time for me both mentally and physically" in a statement read by Det Insp Smith.
"There is still a long way to go but we are moving in the right direction. I will continue to stay as strong as I can until we reach some sort of justice for my beautiful girl, for Toyah," he wrote.
The 24-year-old's mother Vanessa Gardiner thanked police and the community in a statement, which was also read by the detective inspector.
"We thank the community for their ongoing love and support throughout these difficult times. Now we wait patiently for the justice our beautiful daughter Toyah deserves," Ms Gardiner wrote.
Mr Singh flew to India not long after Ms Cordingley 's remains were found, and he was extradited from Victoria to Queensland one day after he arrived in Australia on a flight from New Delhi.
The 38-year-old former nurse appeared calm as he stepped off the plane in handcuffs at the Queensland government airbase in Cairns on Thursday afternoon.
Flanked by four suited detectives, Mr Singh wore grey tracksuit pants, a black tracksuit top and a navy Sikh turban as he was led across the tarmac in 32C heat.
He was ushered into the back of a police four-wheel drive and taken to Cairns Police Station.
Det Insp Smith said she was "relieved" that Queensland police relationships with their federal and international counterparts had resulted in the extradition.
"It is significant to me personally, it's also significant to the people that stand behind me," she said.
"We put trust in the Australian Federal Police, trust in the individual AFP officers that were on the ground in New Delhi - they certainly did not disappoint us.
"They did more for us than we even thought was possible."
Det Insp Smith said Cairns police had never been involved in an operation of this scale, and the QPS also broke new ground in developing ties with Indian police.
"We, obviously faced many challenges during the four-year investigation, and we are very grateful to be at this point today," she added.
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