Miller was arrested by off-duty Eden police officers, Senior Constable Paul Ellis and Senior Constable Andrew Kuzmins, on Monday afternoon at around 3.30pm in Snug Cove.

The arrest ended a two-day, nationwide manhunt for Miller, after a warrant was issued by Victorian Homicide Squad detectives investigating the death of 32-year-old Chinese national Renea Lau in Melbourne’s King’s Domain parklands on Saturday morning.

At Wednesday’s Melbourne court appearance, Legal Aid for Miller, senior lawyer Sarah Pratt, said her client had suffered a drug-induced psychosis and it was his first time in custody.

Police allege Miller raped Renea Lau twice before killing her.

At a media conference in Eden on Monday evening, Acting Inspector Clifton Scarlett said Eden police were on high alert after receiving reports of Miller being sighted nearby.

“We received a call earlier today (Monday) that a male matching this man’s description was sighted about 46km south of Eden,” he said.

“Police were dispatched to that location, but they were unable to locate the male.

“At around 3pm on Monday afternoon two off-duty, uniformed Eden Police officers sighted the suspect asleep on rocks at Snug Cove and he was duly arrested,” he said.

“It was very good work by the two officers.”

Miller was arrested on an outstanding warrant.

“He’s been charged by virtue of an outstanding Victorian warrant and is assisting with enquiries at this moment and will appear in Batemans Bay court first thing in the morning,” Acting Inspector Scarlett said.

Miller was transported to Batemans Bay overnight on Monday, and extradited to Victoria after a court appearance in Bateman Bay Local Court on Tuesday morning.

He did not apply for bail, and conceded to the court that he was the man named in the details of the warrant.

Magistrate Doug Dick approved the extradition of Mr Miller, who was remanded in the custody of two Victorian Police officers, Nathan Toohey and Luke Farrell, from the St Kilda Police homicide squad, for the journey back to Melbourne.

Ms Lau was believed to have been on her way to work on Saturday when she was chased and assaulted in an apparently random attack in Melbourne at about 5.30am, the Homicide Squad’s Detective Inspector John Potter said.

Victoria Police had earlier released images and CCTV of Miller.

It was these images which helped the public to recognise the murder suspect on Monday, south of Eden.

Miller, who had previously lived in Western Australia, was reported to be sleeping on the streets of Melbourne for at least six weeks, and was known to police in other states.