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Tobias Friedrich Moran, formerly known as Tobias Suckfuell, was flown to Sydney on Wednesday, having spent the night at Perth Watch House after a magistrate granted his extradition.
The now 42-year-old had been travelling around Australia with Ms Strobel when her body was found near a Lismore caravan park in 2005.
The 25-year-old schoolteacher had been suffocated with a pillow or plastic bag.
Ms Strobel's murder has remained unsolved despite the establishment of a police strike force and the NSW government offering a $1 million reward in 2020.
On Tuesday, it emerged Moran had been arrested in connection with the case after a NSW warrant was issued.
He has since been charged with murder and acting with intent to pervert the course of justice. Refused bail, he will face Sydney's Downing Centre Local Court on Thursday.
Moran's lawyer Tony Elliott told Perth Magistrates Court his client had no previous known convictions and he was unaware of any other charges or bail proceedings.
Police have previously said they believe Ms Strobel was murdered by Moran, who refused to return to Australia to give evidence at her inquest.
Deputy NSW Coroner Paul McMahon in 2007 found there was insufficient evidence to recommend charges but said he had a "very strong suspicion" Moran, then known as Suckfuell, was involved in the killing.
Ms Strobel had been on a night out with Moran and friends when she was last seen at Lismore Tourist Caravan Park on February 11, 2005.
Her body was found six days later, concealed under palm fronds at a sports ground, less than 100 metres from the caravan park.
Authorities in Germany also offered a reward in 2014 of 10,000 euros to German and Australian residents with any information about Ms Strobel's death.