Fattal and Bauer were released earlier this week from custody and arrived in Oman under a $1 million bail deal.
Iran's Foreign Ministry called it a gesture of Islamic mercy.
Their return to the U.S. will be the end of a long ordeal that started in July 2009 when they were detained along the Iran-Iraq border along with fellow hiker Sarah Shourd. The three always maintained their innocence, saying they were only hiking in Iraq's relatively peaceful Kurdish region and accidentally wandered into Iran.
Shourd, Bauer's fiancee, was released last September on $500,000 following furious diplomatic efforts, as negotiations continued for the two men. In August, Fattal and Bauer were sentenced to eight years in prison each for illegal entry into Iran and espionage.
The first sign of change in the case came last week when Iranian President Mahmoud Ahmadinejad said the two men could be released within days. But wrangling from within the country's leadership delayed efforts. Iranian defense attorney Masoud Shafiei secured the necessary judicial approval Wednesday for the bail - $500,000 for each man.
Hours later, the gates of Tehran's Evin prison opened and the Americans headed in a convoy with diplomats to Tehran's Mehrabad airport.
Until their release, the last previous direct contact family members had with Bauer and Fattal was in May 2010, when their mothers were permitted a short visit in Tehran, which Iranian officials used for high-profile propaganda.
Shourd was with the families to greet the two on the tarmac at a royal airfield near the main international airport in Oman's capital, Muscat.
Shortly before midnight Wednesday, Fattal and Bauer, wearing jeans and casual shirts, bounded down the steps from the plane. The men appeared very thin and pale, but in good health.
"We're so happy we are free," Fattal told reporters in a brief statement before leaving the airport.
"Two years in prison is too long," Bauer said, adding he hoped their release from prison will also bring "freedom for political prisoners in America and Iran."
The Associated Press contributed to this report.