A fourth Iranian American released as part of the arrangement, Nosratollah Khosravi-Roodsari, opted to remain in Iran.
Former U.S. Marine Amir Hekmati who was released by Iran over the weekend says he feels lucky to be free again.
Hekmati's family released a photo Monday showing him with two sisters and a brother-in-law, along with U.S. Rep. Dan Kildee, D-Michigan. "Up until the last second we were all concerned". "It happened to come together at that moment, I think that everybody saw that that would be propitious, but it was not directly linked", he said.
"Why did Iran prisoner swap not include my father?" said Sarah Moriarty.
"I tried my best to keep my head up and withstand all the pressures that were put on me, some of them were very inhumane and unjust", he said. "The Swiss are wonderful".
On his Twitter feed, Mr Kildee shared what he said was a personal message from Mr Hekmati. "They just came one morning and said 'pack your things, '" he said.
Hekmati's release comes four years after an Iranian court sentenced him to death; that verdict was later overturned. "As soon as we got out of Iranian air space, champagne bottles were popped".
Abedini, who was born and raised in Iran before becoming a US citizen five years ago, had established small house churches in Iran. An American student who was freed separately, Matthew Trevithick, 30, flew out Saturday on his own.
He was accompanied out of Tehran by his mother and Iranian wife, also a journalist. Hekmati was detained in August 2011 on espionage charges.
The approval of Khamenei was critical to allow last year's nuclear accord with world powers that limited Tehran's nuclear program in exchange for easing worldwide economic sanctions.
There was no mention of the prisoner swap while the deal was being negotiated. They will be included in the group's annual report to the U.N. Human Rights Council.
Rep. Jared Huffman, from California, expressed thanks to the U.S. State Department for negotiating the men's release. In Iraq, there are Iranian ties with Shiite militias, which could have had a hand in the recent abduction of three Iraqi-American contractors in Baghdad.
Even once the nuclear deal had been announced, Rezaian's own departure from Iran was "touch and go until the last minute". US officials have said they are not sure if he is still alive.
He was picked up in 2014 and accused of spying - charges both the Postand the Obama administration called absurd. He said Iran's missile industries "are fully home-made" and impervious to sanctions, the semiofficial Fars News Agency reported.