Bauer, Fattal, and a third UC Berkeley graduate, Sarah Shourd, were arrested on July 31, 2009, after embarking on a hike in Iraq's Kurdistan region near the Iranian border.
Iran has accused them of espionage, but the hikers and their families say they aren't spies but instead were detained after they accidentally crossed an unmarked border into Iran.
Iran released Shourd, 32, who is engaged to Bauer, last September because she was in poor health.
The Swiss Embassy represents U.S. interests in Iran and has been acting as an intermediary, according to U.S. State Department officials.
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Update Statement from families...
THE FAMILIES OF SHANE BAUER, JOSH FATTAL AND SARAH SHOURD RELEASED THE FOLLOWING STATEMENT TODAY FOLLOWING NEWS OF THEIR RELEASE:
Today can only be described as the best day of our lives. We have waited for nearly 26 months for this moment and the joy and relief we feel at Shane and Josh's long-awaited freedom knows no bounds. We now all want nothing more than to wrap Shane and Josh in our arms, catch up on two lost years and make a new beginning, for them and for all of us. For now, we especially would like to thank His Majesty Sultan Qaboos bin Said Al Said of Oman and his envoy Dr. Salem Al Ismaily; our lawyer, Mr. Masoud Shafii; and the Swiss Ambassador to Iran, Livia Leu Agosti, and her colleagues, for working to make today a reality. At the same time, our deep gratitude extends to many, many others, from governments, institutions and noted campaigners to tens of thousands of people around the world. Their support for Shane, Josh, Sarah and our families has sustained us and comforted us throughout this time. Our appreciation for the warmth and love of our fellow human beings is unending and we know that Shane and Josh will always be grateful."