In the statement, the couple said they were "extremely happy and relieved to be safely back in Australia with those we love", ABC News reported.
The Perth couple had been detained for several months after being arrested for reportedly flying a drone without a permit. They had been travelling around the world since 2017 and documenting their adventures online.
All charges against them have now been dropped.
"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 said.
"While we understand the intense public interest, we do not wish to comment further at this time and request the media let us and our families get back to our 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," the couple added.
Foreign Affairs Minister Marise Payne said the travel bloggers were in "good health and in good spirits" and had been united with their families.
She said the couple's return was a "source of great relief and joy for everyone".
Payne had raised the matter with the Iranian Government at a recent summit, and had been in face-to-face talks with Iran's Foreign Minister Javad Zarif, ABC reported.
Another Australian, Melbourne academic Kylie Moore-Gilbert, remains incarcerated in the same prison.
Moore-Gilbert has reportedly been sentenced to 10 years in jail by Iranian authorities.
( With inputs from IANS )