An Australian couple who spent more than three months detained in Iran have been freed in an apparent prisoner swap deal between the Morrison government and Tehran.

Foreign Minister Marise Payne said on Saturday that Mark Firkin and Jolie King, who is also a British citizen, were in "good health and in good spirits" and they had been united with their families after they were arrested for allegedly flying a drone over a military precinct near Jajrood in Tehran province without a permit.

Following the announcement of the couple's release, Tehran's state media reported an Iranian student detained in Brisbane for 13 months had returned home after being released. He had been fighting extradition to the United States to face conspiracy charges.

University of Queensland PHD student Reza Dehbashi Kivi, 38, faced prosecution in the US for six charges, most relating to the alleged exportation of 20-watt power amplifiers more than 10 years ago.