Attorney-General Christian Porter said in a statement that "in all the circumstances of this particular case" the academic, Reza Dehbashi Kivi, should not be extradited.
"My decision was made in accordance with the requirements of Australian domestic legal processes and is completely consistent with the powers provided to the commonwealth attorney-general under our law," Porter said.
The statement came hours after Iran had agreed to free an Australian couple from a Tehran prison who were held on spying charges. Later on Saturday, Iranian media reported that Dehbashi Kivi had already returned to Iran.
Porter would not say whether the two cases were related.
"The Australian Government does not comment on the details behind its consideration of particular cases," Porter said in his e-mailed statement.
"And while it is likely that because of Mr Kivi's nationality some will speculate regarding this matter, consistent with prior practice I do not intend to comment further on the particular details of this case, particularly when any such response from me may diminish our government's capacity to deal with future matters of this type in Australia's best interests."
According to Australia's ABC News, the 38-year-old Dehbashi Kivi was arrested in September of 2018 on accusations of sending American equipment for stealth planes or missiles to Iran.
The United States sought to extradite him on six charges, including conspiring to export special amplifiers classified as "defence articles" under the US munitions list, according to ABC News.
Dehbashi Kivi was a doctorate student at the University of Queensland, with his lawyer saying he was working on developing a machine to detect skin cancers, according to Australian media reports.