In a rare prisoner swap the United States and Iran each freed a prisoner from detention.
Donald Trump said Xiyue Wang, a US citizen held in Iran for three years on spying charges, was returning to the United States.
An Iranian official said that Iranian Massoud Soleimani had been freed from detention in the United States.
Switzerland facilitated the swap and Iranian state news agency IRNA said Foreign Minister Mohammad Javad Zarif welcomed Mr Soleimani in Zurich, where it reported the swap took place.
Mr Soleimani was expected to return to Iran in the coming hours.
In a statement issued by the White House, the US President made no mention of the freeing of Mr Soleimani.
However, he thanked the Swiss government for its help in negotiating Wang's release.
"Freeing Americans held captive is of vital importance to my Administration, and we will continue to work hard to bring home all our citizens wrongfully held captive overseas," he said.
Earlier, Mr Zarif the prisoner swap was imminent. Later he posted pictures on Twitter of himself with Mr Soleimani talking on board an Iranian plane.
"Glad that Professor Massoud Soleimani and Mr. Xiyue Wang will be joining their families shortly. Many thanks to all engaged, particularly the Swiss government," he tweeted.
Switzerland represents US diplomatic interests in Iran, since Washington and Tehran cut diplomatic ties shortly after the 1979 Islamic Revolution in Iran.
Mr Wang, a Princeton University graduate student, was convicted on espionage charges and sentenced to 10 years in prison in 2017.
His family and the university have always said he was in Iran for research into a history degree and denied spying.
Reporting by agencies.
