Muscat, Oman (CNN) -- American hikers Josh Fattal and Shane Bauer bounded down the steps of the aircraft that took them from Iran to Oman late Wednesday, rushing into the arms of loved ones who had sought their freedom for more than two years.
The pair, released earlier in the day from an Iranian prison, arrived in Muscat, the capital of Oman.
Their families and hiker Sarah Shourd -- who was arrested with them but freed last year on medical grounds -- hugged the young men. Shourd is Bauer's fiancee.
Before leaving the Muscat airport for an undisclosed location, Fattal and Bauer released brief statements. They took no questions from reporters.
"We're so happy we are free and so relieved we are free," said Fattal. "Our deepest gratitude goes toward his majesty Sultan Qaboos of Oman for obtaining our release. We're sincerely grateful for the government of Oman for hosting us and our families."
Bauer said: "Two years in prison is too long and we sincerely hope for the freedom of other political prisoners and other unjustly imprisoned people in America and Iran."
The families earlier expressed their joy, relief and gratitude at the pair's release.
"Today can only be described as the best day of our lives," they said in a statement. "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."
President Barack Obama also welcomed the "wonderful news," saying he was thrilled and could not feel happier for the two men's families. He thanked Oman, Iraqi President Jalal Talabani and the Swiss government for their assistance.
Fattal and Bauer were released earlier Wednesday on bail of $500,000 each and their sentences for spying convictions were commuted, Iran's judiciary said, according to government-run Press TV. The departure of the two from Iran effectively meant the bail money will be forfeited and kept by Iran.
The lawyer for Fattal and Bauer, Masoud Shafiee, told CNN the $1 million bail had been paid by the Omani government.
Fattal spoke with his brother, Alex, by phone after the release, according to a source familiar with the hikers' release who asked not to be identified.
The family has not yet said how long everyone will stay in Oman before heading to the United States.
Shourd is no longer wearing an engagement ring Bauer made from a thread from one of his shirts while they were in prison together because she had lost the ring while traveling round the United States working for the release of her fiance and Fattal, said Samantha Topping, a spokeswoman for the families.
Oman's envoy to Tehran, Salem al Ismaily, earlier said in a statement the pair were in the custody of the Omani government and would spend a couple of days in Muscat "before heading home."
U.N. Secretary-General Ban Ki-moon appreciates "the decision of the Iranian authorities to positively respond to international appeals on humanitarian grounds," according to a statement. "He commends all parties who helped to secure their release."
Fattal and Bauer arrived at Tehran's Mehrabad International Airport late Wednesday in a convoy of diplomatic cars. The convoy had earlier left the country's notorious Evin Prison through the front gates, accompanied by a police escort, but Bauer and Fattal were not visible.
Swiss and Omani officials had waited outside the prison to receive the Americans. Switzerland represents U.S. interests in Iran because there is no American embassy there, and Oman has acted as a broker between Washington and Tehran in the past.
Oman helped secure the release of Shourd, posting her bail last September, a senior Obama administration official said at the time.
The two men's release comes a day before Iranian President Mahmoud Ahmadinejad is due to speak at the United Nations General Assembly in New York.
Asked at the United Nations about the news, Ahmadinejad's chief of staff, Esfandiar Mashaei, said: "Yes, we were expecting their release, us and the president."
High-profile American Muslims including boxing legend Muhammad Ali had called for their release, and a high-profile delegation of American Christian and Muslim religious leaders met Ahmadinejad in Iran last week to plead for their freedom.
"We were very happy to learn about their release today," said Nihad Awad, national executive director of the Council on American Islamic Relations (CAIR), who was part of the delegation to Tehran. "We are extremely happy for the hikers, their families and the country."
Bauer and Fattal, both 29, were convicted last month of entering Iran illegally and spying for the United States, and each was sentenced to eight years in prison.
Their attorney, Shafiee, went into the prison earlier Wednesday with paperwork to show that bail had been paid for each of them. A judge had signed the bail papers that morning after several days of delays.
Fattal and Bauer were arrested along with Shourd in July 2009 after apparently straying over an unmarked border between Iraqi Kurdistan and Iran.
Bauer and Shourd told their families in May last year that they had gotten engaged in prison and planned to get married after their release. Fattal plans to be best man at the wedding, the hikers' relatives said in a statement at the time.
Shourd, in an interview with CNN a year ago, said Bauer had asked her to marry him while they were imprisoned so that they could have something to sustain them through their days in Evin, and give them hope for their future together.
Shourd was freed almost exactly a year ago on medical grounds. Her release came a week before Ahmadinejad addressed the U.N. last year.
One analyst said the timing last year was no coincidence.
"I think President Ahmadinejad really wanted to use this as a way of building up a store of goodwill just before he comes to New York," Columbia University Prof. Gary Sick said last year after Shourd came home.
The Americans say they accidentally crossed into Iran when they veered off a dirt road while hiking near a tourist site in the Kurdish region of northern Iraq. They denied the charges and appealed the sentence while serving time in prison.
Ahmadinejad said last week that the release of Fattal and Bauer was imminent, setting off a roller coaster ride of expectations.
The judiciary shot back that only it could make decisions about their release.
An Omani official flew to Iran on September 14 to help work on any negotiation, a Western diplomat told CNN at the time.
CNN's Elise Labott, Mohammed Jamjoom, Shirzad Bozorgmehr, Richard Roth, Mitra Mobasherat and Susan Candiotti contributed to this report.