Tehran announced the release of Iranian scientist Massoud Soleimani from the United States shortly before Washington declared American researcher Xiyue Wang was returning home.
"Glad that Professor Massoud Soleimani and Mr. Xiyue Wang will be joining their families shortly," Iran's Foreign Minister Mohammad Javad Zarif tweeted.
"Many thanks to all engaged, particularly the Swiss government," which has looked after US interests in Iran in the absence of diplomatic ties, Zarif said.
In a statement issued in Washington, US President Donald Trump said that "after more than three years of being held prisoner in Iran, Xiyue Wang is returning to the United States".
Secretary of State Mike Pompeo said the US was "pleased that Tehran has been constructive in this matter" while also thanking Switzerland for its role.
A statement on the Iranian judiciary's Mizan Online website said Wang had been "freed on Islamic clemency" and handed over to Swiss officials in order to be returned to America.
Wang, a Chinese-born American, was serving 10 years on espionage charges in Iran.
A doctoral candidate in history at Princeton University, he had been researching Iran's Qajar dynasty when he was imprisoned in August 2016.
Iran's state news agency IRNA said Soleimani had been "freed moments ago after one year of illegal detention and was handed over to Iranian officials in Switzerland".
Soleimani, a professor and senior stem cell researcher at Tehran's Tarbiat Modares University, was arrested on arrival at Chicago airport in October 2018 for allegedly attempting to ship growth hormones, according to Iranian media.
"Going home," Zarif said in another tweet.
The Twitter post featured photos of the foreign minister alongside Soleimani outside and inside a plane bearing an Iranian flag. It was unclear when the picture was taken.
Spying allegations
The United States and Iran have not had diplomatic ties since 1980.
Relations between the two foes worsened in May 2018 when Trump withdrew the US from an international accord that gave Iran relief from sanctions in return for curbs on its nuclear programme.
Iran retaliated one year later by suspending some of its commitments under the nuclear pact.
The arch-enemies came to the brink of a military confrontation in June this year when Iran downed a US drone and Trump ordered retaliatory strikes before cancelling them at the last minute.
Iran has over the years arrested several foreign nationals most often on accusations of spying.
They include former US soldier Michael R. White, British-Iranian mother Nazanin Zaghari-Ratcliffe, French academic Roland Marchal and Australian university lecturer Kylie Moore-Gilbert.
Two other Australians, travel bloggers Jolie King and Mark Firkin, were released in October by Iran, in another apparent prisoner swap for Iranian student Reza Dehbashi, who had been wanted in the United States.
In September, an Iranian woman sentenced in the United States for violating Washington's sanctions against Tehran was released and returned home.
Negar Ghodskani was arrested in Australia in 2017 and later extradited to the United States, which said she confessed to participation in a conspiracy to illegally export technology to Iran in breach of sanctions.
Pregnant at the time of her arrest, she was sentenced to 27 months but released after already serving time in custody.
An unknown number of Iranians are detained abroad.
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