The English-language Press TV reported only that Shourd, 32, had been released "on a bail of $500,000" but did not specify whether the money had been paid or give more details. Her family had said it was having difficulty raising the money.
Her lawyer, Masoud Shafiei, said Shourd had been released but was still undergoing formalities inside the Evin Prison, where she has been held in solitary confinement. He said he had no information about her departure route or any details about bail.
A spokesman for the Swiss Foreign Ministry, Lars Knuchel said the release had not been formally confirmed but "we are very confident that things are moving into the right direction."
The U.S. broke off ties with Iran after the 1979 Islamic Revolution, and Switzerland handles U.S. interests in Iran.
Shourd and her two friends -- Shane Bauer and Josh Fattal -- were detained along the Iran-Iraq border on July 31, 2009 and accused of illegally crossing the border and spying in a case that has deepened tensions with Washington. Their families say they were hiking in Iraq's scenic north, and that if they crossed the border, they did so unwittingly.
Iran's judiciary issued a statement saying the "pretrial detention" of the two American men has been extended for two more months.
The stage was set for Shourd's release last week when Ahmadinejad said he intervened as a gesture of Islamic compassion at the end of the holy month of Ramadan. However, the judiciary quickly humbled the president by saying it was in charge of the case and would set the rules -- in the form of the largest known bail for any high-profile Westerner jailed in the past year.
Shortly after judicial officials announced the bail on Sunday, Shourd's lawyer predicted she could walk free in "two or three days."
Shourd's mother says she has serious medical problems, including a breast lump and precancerous cervical cells.
Moves to release Shourd have been accompanied by political jockeying in Iran between Ahmadinejad and his more conservative rivals.
Nora Shourd's phone message box was full when the AP tried reaching her for comment. A New York publicist working with the families, Samantha Topping, did not immediately return a phone call seeking comment. A message on the cell phone of Cindy Hickey, mother of Shane Bauer, referred calls to Topping.