Daniel Duggan, 57, has been held in prison since his arrest in a rural town in New South Wales state in 2022, shortly after he returned from living in China for close to a decade as an aviation consultant.
His arrest came days after Britain warned its former military pilots not to work for a South African flight training school that was training large numbers of Chinese pilots, where Duggan had worked a decade earlier.
Duggan has denied the charges.
Outside the court on Thursday his wife Saffrine said she was disappointed with the ruling and urged Prime Minister Anthony Albanese to stop the extradition.
A 2017 indictment in the United States, unsealed after his arrest, showed Duggan was one of several former military pilots linked to the South African company and a Chinese recruiter who were alleged to have broken US law.
Duggan moved to China from Australia in 2013.
His lawyers have previously said he was barred by China from leaving in 2014, and came to fear for his family's safety.
He has been held in a maximum security prison since his arrest.