JOIN USIran's state news agency IRNA said Shane Bauer and Josh Fattal left Iran just as darkness fell in the capital.
An Omani official told The Associated Press the men were flying to the capital Muscat.
He spoke on condition of anonymity because he was not authorised to speak to the media.
He did not say how long the two men will stay in the Gulf state before heading home to America.
The case of Bauer and Fattal, who were convicted by an Iranian court of spying for the United States, has deepened strains in the already fraught relationship between Washington and Tehran.
Iranian President Mahmoud Ahmadinejad, who was first to mention last week that the Americans' could be released, is in the US and is scheduled to speak at the United Nations General Assembly tomorrow.
The release came just minutes before President Barack Obama addressed the UN General Assembly.
There was no direct evidence that Iran timed the American's freedom to overshadow Obama's speech, but Iran has conducted international political stagecraft in the past.