The three arrived on a flight at Ramstein Air Base and were scheduled to undergo medical checkups at Landstuhl Regional Medical Center, a U.S. military hospital.
Earlier Sunday, the group made a stop in Switzerland. A U.S. State Department envoy posted a photo that appeared to show Rezaian standing on a tarmac outside a plane there.
The fourth prisoner released in the swap, identified by U.S. officials as Nosratollah Khosravi-Roodsari, decided not to leave Iran, senior White House officials said. "It's his free determination" whether he wants to stay in Iran, one official said. "We don't make that judgment."
White House officials said earlier Sunday that recently detained student Matthew Trevithick also was released -- but not as part of the prisoner swap -- and had left Iran. There were no additional details.
The five Americans had been detained in separate cases, some as early as 2011.
Return eagerly awaited
The Washington Post's executive editor and foreign editor told CNN that they were in Germany to meet with Rezaian.
"I'm relieved, but I'm also elated. I remember the morning a year and a half ago when a scratchy cell phone call told me Jason and his wife had been taken from their apartment the night before," said Doug Jehl, the newspaper's foreign editor. "We never could have believed that this nightmare would go on for so long, but I'm just overjoyed that it's about to be over."
In a memo to the newspaper's staff, the editors said they spoke with Rezaian on the phone Sunday night while he was at the hospital next-door. Asked how he was doing, according to the memo, Rezaian said, "I'm a hell of a lot better than I was 48 hours ago."
An 11th-hour disagreement over whether Rezaian's mother was on board the flight delayed the plane's departure, a U.S. official said, but Secretary of State John Kerry said in an interview with The Washington Post that Iranian Foreign Minister Javad Zarif assigned four people to help resolve the dispute.
Naghmeh Abedini, the pastor's wife, said on Twitter that she was hoping to talk with her husband in a few hours. In the meantime, she spoke on the phone with President Barack Obama.
Iranian, dual citizens freed in U.S.
In exchange for the American prisoners' freedom, the United States pardoned or commuted the sentences of an Iranian and six dual citizens of the United States and Iran
in what Obama called a "one-time gesture."
The men allegedly had been involved in exporting products and services to Iran in violation of trade sanctions against the country. They were accused of exporting goods ranging from electronic components and satellite services to marine navigation and military equipment to Iran.
Khosrow Afghahi, Tooraj Faridi, Bahram Mechanic and Nima Golestaneh were pardoned. Nader Modanlo, Arash Ghahreman and Ali Saboonchi had their sentences commuted, the U.S. Justice Department said
Obama praised the "tireless" effort that went into the prisoner exchange, which comes a day after international inspectors concluded Tehran was in compliance
with the deal governing its nuclear program. Iranian officials and U.S. administration officials confirmed the news Saturday. As a result, some international economic sanctions against Iran were lifted.
The deal came after more than a year of secret negotiations, the officials said. The nuclear agreement "accelerated" the prisoner swap, Kerry said.
The United States also agreed to drop charges against 14 other Iranians whose extradition to the United States seemed unlikely, a U.S. official said.
Congressmen to meet freed prisoners
Two congressmen were headed to Germany to greet Rezaian and Hekmati.
"I am thrilled and relieved that Jason and these other Americans are no longer in prison," said Jared Huffman, who represents Rezaian and has been involved in his case.
Huffman said the freed prisoners won't be on U.S. soil for a few days, he said.
Rep. Dan Kildee, D-Michigan, said Hekmati's father had fallen ill in the more than four years that his son has been detained. There is hope "that having Amir back gives him some strength."
He said family members were feeling "tempered jubilation" while they waited to find out if Hekmati was really released, because they've gotten their hopes up in the past.
"Until he was out of Iran, until I got a call from the White House today saying the plane has crossed Iranian border, he is out of Iran, we all took a deep breath. Because it all became real," the congressman told CNN.
In a statement, Kildee addressed Hekmati, saying, "Amir, I cannot wait to meet you for the first time, give you a big hug, and welcome you home."
Robert Levinson's fate unknown
Trevithick's release was not part of the prisoner swap, but U.S. officials did "indicate to Foreign Minister Zarif that it'd be important for them to try to resolve some of the other cases of Americans detained in the context of this 'deal,'" a senior administration official told CNN.
During negotiations, another American's name was apparently on the table: Robert Levinson
Iran has denied holding Levinson, a former FBI agent and CIA contractor who went missing there in 2007.
Now the agreement between the United States and Iran calls for Iranian officials to "continue cooperating with the United States to determine the whereabouts of Robert Levinson," a U.S. official said.
Kerry said Sunday that Iran had agreed to deepen coordination in the search.
"We are happy for the other families," Levinson's family said in a statement. "But once again, Bob Levinson has been left behind. We are devastated."