An Australian professor detained in Iran for 804 days for espionage has returned home following a reported swap for three Iranians jailed abroad.

In statements shared on social media, Kylie Moore-Gilbert thanked Australian officials and supporters who worked "tirelessly" to get her home.

Moore-Gilbert, a professor of Middle Eastern studies, was arrested in 2018 after attending an educational conference in Iran. She was stopped in Tehran airport and hauled to jail over claims she was a spy, allegations she has always denied. She was sentenced to 10 years.

Reports Friday, citing government sources, said Moore-Gilbert was targeted after Iranian official discovered she was in a relationship with an Israeli. This claim fueled their belief she was a spy.

An Iranian news outlet affiliated with state television first reported that the three Iranians traded for Gilbert included one businessman and two citizens "detained abroad," according to the BBC.

The Sydney Morning Herald said those Iranians were identified as Saeed Moradi, Mohammad Khazaei and Masoud Sedaghat Zadeh, who were held in Thailand after a 2012 failed bomb attack targeting Israeli diplomats.

Video released as the swap occurred showed Moore-Gilbert, wearing a gray headscarf and a blue face mask, being placed in a white van. The same video showed the three Iranian prisoners being welcomed back to Iran. One man was in a wheelchair and all three wore the Iranian flag draped over their shoulders, black baseball caps and masks covering their faces.

Prime Minister Scott Morrison declined to confirm or deny that a prisoner swap was made.

"Australia works through diplomatic channels to resolve many issues of this nature, so it would not be in Australia's interests or for the safety of other Australians who, from time to time may find themselves in this situation, Morrison said during a news conference with reporters.

Morrison and Marise Payne, Australia's minister for foreign affairs, expressed delight in Moore-Gilbert's return home.

"The Australian Government has consistently rejected the grounds on which the Iranian Government arrested, detained and convicted Dr Moore-Gilbert," Payne said in her statement.

Throughout the imprisonment, groups such as "Free Kylie Moore-Gilbert" pressured government officials to coordinate her release. The account for that groupposted on Twitter the day of her release, calling on Morrison to act, unaware that a deal was being stuck.

A few months before her release, Moore-Gilbert was reportedly sent to Qarchak women's prison, an overcrowded jail located in a remote desert, where prisoners experience harsh conditions, according to the Human Rights Activists News Agency.

Moore-Gilbert had written to the Australian government to implore them to work harder for her release. In letters, she wrote that she had been subjected to "grievous violations" of her rights and psychological torture.

Amnesty International Australia called for an investigation into Gilbert's allegations.

"Her allegations of torture and other ill-treatment, including through prolonged solitary confinement, must be independently and effectively investigated by the Iranian authorities and anyone found responsible brought to justice in fair trials," Amnesty International Australia Individuals at Risk campaigner, Rose Kulak, said.

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