TEHRAN, Iran — Two Americans jailed in Iran as spies left Tehran on Wednesday, closing a high-profile drama with archfoe Washington that brought more than two years of hope then heartbreak for the families as the Islamic Republic’s hard-line rulers rejected international calls for their release.

Iran’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 authorized 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 United States and is scheduled to speak at the United Nations General Assembly on Thursday.

The release came just minutes before President Barack Obama addressed the U.N. 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.

Most famously, Iran waited until just moments after Ronald Reagan’s presidential inauguration in January 1981 to free 52 American hostages held for 444 days at the former U.S. Embassy after it was stormed by militants backing Iran’s Islamic Revolution. The timing was seen as a way to embarrass ex-President Jimmy Carter for his backing of Iran’s former monarch.

Associated Press reporters saw a convoy of vehicles with Swiss and Omani diplomats leaving Evin prison on Wednesday afternoon with Shane Bauer and Josh Fattal inside, heading to Tehran’s Mehrabad airport.

Switzerland represents American interests in Iran because the U.S. has no diplomatic relations with Tehran and the prisoners are expected to be flown to Oman now.

The two men, both 29, were driven out of the prison compound just minutes after their Iranian attorney, Masoud Shafiei, said he has completed the paperwork for their release.

“I have finished the job that I had to do as their lawyer,” Shafiei said. He obtained signatures of two judges on a bail-for-freedom deal. A $1 million bail — $500,000 for each one — was posted.

Police vehicles escorted the convoy of Swiss and Omani vehicles, carrying the two Americans to Mehrabad airport, which was once Tehran’s main gateway to the world but is now used for domestic flights. The airport is near the massive Azadi Square, which Iran uses to hold military parades but also was a temporary hub for protesters after Ahmadinejad’s disputed re-election in 2009.

Bauer and Fattal were arrested along the Iran-Iraq border in July 2009 and sentenced last month to eight years each in prison. A third American arrested with them, Sarah Shourd, was freed last year on bail.

The London-based rights group Amnesty International called the release of the Americans a “long overdue step.”

“Iranian authorities have finally seen sense” and have agreed to release Shane Bauer and Josh Fattal, said Hassiba Hadj Sahraoui, Amnesty International Deputy Director for Middle East and North Africa. “They must now be allowed to leave Iran promptly to be reunited with their families.”

The three Americans — friends from their days at the University of California at Berkeley — have maintained their innocence and denied the espionage charges against them.

Their families and the U.S. government said they were just hiking in northern Iraq’s scenic and relatively peaceful Kurdish region when they may have accidentally strayed over the unmarked border with Iran.

The last direct contact family members had with Bauer and Fattal was in May 2010 when their mothers were permitted a short visit in Tehran.

It was not clear where the two men will be reunited with their families after their release.

Phone messages left for Fattal’s mother and brother in Philadelphia were not immediately returned Wednesday.

Since her release last year, Shourd has lived in Oakland, Calif. Bauer, a freelance journalist, grew up in Onamia, Minn., and Fattal, an environmental activist, is from suburban Philadelphia.

Bauer proposed marriage to Shourd while in prison.

After her release last September, Shourd was flown on a private plane to the Omani capital, Muscat.

Last week, Oman again dispatched a plane belonging to the Gulf country’s ruler to the Iranian capital to fetch the two men if the freedom-for-bail was reached.

Oman has close ties with both Tehran and Washington and plays a strategic role in the region by sharing control with Iran of the Strait of Hormuz at the mouth of the Persian Gulf, which is the route for 40 percent of the world’s oil tanker traffic.

Their case of the three Americans closely parallels that of freelance journalist Roxana Saberi, an Iranian-American who convicted of spying before being released in May 2009. Saberi was sentenced to eight years in prison, but an appeals court reduced that to a two-year suspended sentence and let her return to the U.S.

In May 2009, a French academic, Clotilde Reiss, also was freed after her 10-year sentence on espionage-related charges was commuted.

Last year, Iran freed an Iranian-American businessman, Reza Taghavi, who was held for 29 months for alleged links to a bombing in the southern city of Shiraz, which killed 14 people. Taghavi denied any role in the attack.

The possible release of the two Americans would remove one point of tension between Iran and the United States, but suspicions still exist on both sides and no thaw is in sight.

Washington and European allies worry Iran is using its civilian nuclear program as cover to develop atomic weapons and have urged for even stronger sanctions to pressure Tehran. Iran denies any efforts to make nuclear weapons.

Iran, meanwhile, is deeply concerned about the U.S. military on its borders in Iraq and Afghanistan, and sharply denounces U.S. influence in the Middle East.