Scott Allen Miller appeared in Batemans Bay Local Court on Tuesday after he was arrested in relation to the death of Chinese national in Melbourne on Saturday.
Mr Miller was apprehended on Monday after a warrant for his arrest was issued in Victoria.
He was led into the court in handcuffs, appeared alert, and had his long hair tied in a small bun at the back of his head.
He did not apply for bail.
He 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 is to be remanded in the custody of two Victorian Police officers, Nathan Toohey and Luke Farrell, from the St Kilda Police homicide squad.
He is due to appear in the Melbourne Magistrates Court on July 2.
Batemans Bay Local Court confirmed Mr Miller had not yet been charged at the time of his court appearance.
A nationwide search was launched for Mr Miller after the body of a 32-year-old Chinese woman was found in parkland near the intersection of St Kilda Road and Linlithgow Avenue early on Saturday.
The 42-year-old itinerant, who has lived in Western Australia, was arrested in Eden on Monday afternoon.
Off-duty police had spotted Mr Miller sleeping on rocks in Eden's Snug Cove wharf precinct and arrested him about 3.30pm.
He was held in custody and is scheduled to appear in a Batemans Bay court.
The woman was believed to have been on her way to work on Saturday when she was chased and assaulted in an apparently random attack about 5.30am, the Homicide Squad’s Detective Inspector John Potter said.