Iran spies
Shane Bauer and Josh Fattal, both 29, were flown to Oman after being freed on bail from Evin prison.
They were sentenced in September to eight years in prison on charges of spying.
They were arrested in 2009 after crossing into Iran from Iraq, where they said they were hiking.
'Healthy and strong'
"We are so happy we are free and so relieved we are free," Mr Fattal said to reporters soon after their arrival on Wednesday in the Omani capital, Muscat.
Mr Bauer added: "Two years in prison is too long and we sincerely hope for the freedom of other political prisoners and other unjustly imprisoned people in America and Iran."
Also waiting on the tarmac was Sarah Shourd, 32, a third US hiker who was with Mr Bauer and Mr Fattal when they were arrested.
Ms Shourd became engaged to Mr Bauer while they were in prison, before she was freed last year on humanitarian grounds and returned home.
Soon after he was reunited with his son, Mr Fattal's father told reporters: "They are healthy, happy and strong."
Iran's judiciary reportedly set each bail at five billion rials ($500,000). Oman paid bail of a similar amount for the release of Ms Shourd last year.
The Gulf state of Oman is a US ally which has good relations with Iran.
'Strayed accidentally'
Mr Bauer and Mr Fattal were taken from the prison as part of a convoy of Iranian, Swiss and Omani cars.
Mr Bauer and Mr Fattal have always maintained they strayed into Iran accidentally while walking in the poorly marked border region.
The trio were arrested in July 2009 after travelling to the Kurdistan region of Iraq for a week's holiday.
They were held by Iranian troops who told them they were in Iranian territory.
Mr Bauer and Mr Fattal were convicted in September of espionage and illegal entry. Ms Shourd pleaded not guilty in absentia, but did not return to stand trial, citing ill health.
Earlier this month, Iranian President Mahmoud Ahmadinejad said Mr Bauer and Mr Fattal would be released in days, but officials later denied any decision had been reached.
Their liberation came a day before Mr Ahmadinejad was expected in New York for a meeting of the UN General Assembly.
The case heightened tensions between the US and Iran.
US President Barack Obama said in a statement he was "very pleased" by their release.
"The tireless advocacy of their families over these two years has won my admiration, and is now coming to an end with Josh and Shane back in their arms," he added.
US Secretary of State Hillary Clinton also welcomed the Iranian authorities' decision to free the men.
Source:bbc
