"I want to really offer my thanks to everyone in the world, all of the governments, all of the people that have been involved," said Shourd, 32. "And I especially, particularly want to address President Ahmadinejad, and all of the Iranian officials ... and the religious leaders, and thank them for this humanitarian gesture.
"I'm grateful, and I'm very humbled by this moment," she said.
The families of all three hikers released a statement Thursday, saying they "applaud the Iranian authorities for showing compassion in Sarah's case and again call on them to do the only right thing and release Shane and Josh immediately."
Laura Fattal, the mother of Josh Fattal, said that her only mission is to bring the two remaining hikers home.
"We believe in our hearts they [Iran] will have this compassion to release both kids and we hope as soon as possible."
Tehran's prosecutor offered little hope for the two jailed hikers, saying Thursday they will now be tried for spying.
President Obama said Tuesday he was "very pleased" by Shourd's release, and called for the release of the other two hikers in a statement, saying they "have committed no crime."
"We remain hopeful that Iran will demonstrate renewed compassion by ensuring the return of Shane, Josh and all the other missing or detained Americans in Iran," Obama said.
The State Department said that the willingness to release Shourd proved Iran's ability to "resolve" all the hikers' cases.
Iranian officials, including Ahmadinejad, had announced last week that Shourd would be released on Sept. 11.
Officials in Iran's judiciary canceled Shourd's release last Friday, but reversed themselves on the condition that her family post $500,000 bail, according to an Iranian prosecutor who spoke to Iran's IRNA news agency.
A "bank guarantee" for the bail had been given, an attorney for the hiker's Masoud Shafie, told ABC News.
"The case inspector informed the Tehran prosecutor of a bank guarantee concerning the posting of bail and after the prosecutor's agreement, he issued the order for her freedom," the prosecutor's website said Tuesday, according to PressTV Iran.
The report did not say who was responsible for the guarantee, but two U.S. officials told ABC News Iran had received "assurances" from the country of Oman concerning the bail money.
A senior U.S. official familiar with the negotiations told ABC News Monday that the U.S. government would not be contributing any cash for Shourd's release.
ABC News' Jason Stine, Kirit Radia, Sabrina Parise, Thea Trachtenberg and The Associated Press contributed to this report.