Alex Reuben McEwan has been sentenced to life in prison after being found guilty of murdering Korean student Eunji Ban as she walked to work in Brisbane in November, 2013.

McEwan had admitted killing Ban but pleaded not guilty to murder, arguing diminished responsibility on the grounds mental illness left him unable to control himself.

McEwan testified being possessed by a demon when he attacked Ban near her Roma Street Parklands unit in the early hours of the morning. He dragged her body up stairs to the nearby Wickham Park before dumping it by a tree.

His chilling confession in the back of a police car was caught on camera and played to the court during the trial.

Alex McEwan (left) has been found guilty of the murder of Eunji Ban. (Supplied)

McEwan, wearing a blue forensic suit, described how he had been "thinking really sick thoughts, really feral stuff".

"And on the night of the murder, I just woke up randomly and did it," he said.

"Probably sounds like a load of s---... but, ah, I was kinda waiting for it my whole life... to kill someone".

The Brisbane Supreme Court trial heard from three psychiatrists who believe McEwan wasn't suffering the affects of schizophrenia at the time of the killing and that he only developed the mental illness afterwards.

The judge sentenced McEwan to life in prison with the possibility of parole in 2033.

"You knew what you were doing and you knew it was wrong," Justice Roslyn Atkinson said in sentencing him.

Hyeong-Gyu Ban (left) and Suk Bun Jung (right), the parents of murdered South Korean student Eunji Ban outside court. (AAP)

"Nevertheless, you gave in to your sadistic and violent fantasies and carried out this terrible crime."

Members of Ban's family embraced each other and shed tears as the verdict was delivered.

The sister of twin brothers, Ban had arrived in Australia six weeks before her death, leaving Korea to improve her English to realise her dream of becoming a microbiologist. She died on her brothers' birthday.

Speaking through an interpreter outside the court, Ms Ban's mother Suk Bun Jung spoke of her pain and the hole that had been left in her life and her heart.

"My Eunji, please help me. If I have to carry on with beautiful memories of us, you have to help me so I can be strong enough to carry on," she said.

"I'm still very, very sad."

McEwan, from inner Brisbane suburb Spring Hill, had been drinking with friends the night before the killing, waking up the next day and walking the streets near Ban's home. He randomly attacked her before she could scream or fight back.

The trial heard Ban was beaten so badly she drowned in her own blood.

"She was a visitor from a foreign country. She was just doing something completely normal," Justice Atkinson said.

"You decided to go out and kill someone. You ... picked out someone for no reason at all, apart to act on your violent and sadistic urges and committed the most brutal, horrible crime."

McEwan will remain behind bars at least until late 2033, with time already served and a mandatory non-parole period of 20 years.