The couple, Jolie King and Mark Firkin, spent almost three months in Tehran's Evin prison after they were arrested for flying a drone near a military zone without a license.
In a possible swap, an Australian-British blogger and her fiancé returned home on Saturday after being freed from a three-month detention in Iran.
The couple, Jolie King and Mark Firkin, returned to Australia after all charges against them were dropped.
At the same time, Iran's state TV reported that an Iranian scientist, Reza Dehbashi, who was detained for 13 months in Australia over purchasing a defence system for his country from the US, had returned home.
"We are extremely happy and relieved to be safely back in Australia with those we love," the Australian couple said in a statement. "While the past few months have been very difficult, we know it has also been tough for those back home who have been worried for us."
They thanked the Australian government for helping secure their release.
There was no immediate acknowledgment on Saturday by Iranian officials or in the country's state media of the couple's release. However, that has happened in previous cases.
Iranian TV said that the Australian judiciary had planned to send Dehbashi to the US but that he was released through Tehran's diplomatic efforts.
The couple spent almost three months in Tehran's Evin prison after they were arrested for flying a drone near a military zone without a license.
Before their arrest, they had been globe-trotting for two years and documenting their travels on Instagram and YouTube.
They requested privacy as they seek to "get back to (their) normal lives."
"We know there are others who remain in detention in Iran, including a fellow Australian, and believe intense media coverage may not be helpful for efforts to bring them home," they said.
Foreign Minister Marise Payne said the government continued to seek the return of a third Australian, Melbourne University lecturer Kylie Moore-Gilbert, who has been in detention since October 2018.
Payne described her situation as "very complex".
"She has been detained for some considerable time and has faced the Iranian legal system and has been convicted and sentenced," Payne said, adding the government did not accept the spying charges against her.