Jolie King, a British-Australian travel blogger who was imprisoned in Iran with her fiancé on spying charges, has been released from jail.

Australian foreign minister Marise Payne said yesterday it was "with some enormous relief" that she could announce Ms King and her Australian partner Mark Firkin "have been released and returned" and all charges against them dropped.

"They are in good spirits and they are in good health," she added.

Their release was followed hours later by reports on state media in Tehran that an Iranian student held in Australia and wanted in the United States had also been released and returned home.

Iranian state television showed footage of what it said was Reza Dehbashi arriving at Tehran's Imam Khomeini International Airport and hugging a tearful woman apparently from his family.

Australia's attorney general Christian Porter confirmed in a statement that he had stopped the extradition of Mr Dehbashi, a PhD student at the University of Queensland, to the US. Mr Dehbashi had been detained in Australia for 13 months on accusations of circumventing US sanctions on military equipment.

But Mr Porter dismissed "speculation" over the case amid media reports that it could be part of a prisoner swap involving the bloggers.