Jason Rezaian, 39, was convicted of espionage in Iran in 2015.
Iranian state TV named the other three as Saeed Abedini, Amir Hekmati and Nosratollah Khosravi.
Iran said they were being swapped for seven Iranians held in American prisons but there was no immediate US confirmation.
The Iranian state news agency listed the seven as Nader Modanlo, Bahram Mechanic, Khosrow Afghani, Arash Ghahreman, Tooraj Faridi, Nima Golestaneh and Ali Saboun.
In addition, Iranian state TV said 14 Iranians sought by the US would be removed from an Interpol wanted list.
News of the releases came after Iranian Foreign Minister Javad Zarif predicted that international sanctions against his country would be lifted on January 16.
Javad Zarif is in Vienna for talks with Secretary of State John Kerry over Iran’s nuclear deal.
The international nuclear watchdog, the IAEA, is expected to confirm that Iran has scaled back its atomic activities in line with the agreement.
Billions of dollars of frozen Iranian assets are expected to be released and the sale of Iranian oil on the world market will again be permitted.
Lifting sanctions would unfreeze billions of dollars of assets and allow Iranian oil to be sold internationally.
Jason Rezaian, the Washington Post‘s Tehran correspondent, had been detained in Iran for more than a year before his sentencing last November. The WP has dismissed the charges as absurd.
Saeed Abedini, 35, is a Christian pastor who had been imprisoned since July 2012 for organizing churches in people’s houses.
Amir Hekmati, 32, is a former Marine who spent more than four years in prison on spying charges following his arrest in August 2011 during a visit to see his grandmother.
The detention of Khosrawi had not been previously released.
The Associated Press news agency had named the fourth prisoner known to be held in Iran as Siamak Namazi, a businessman and the son of a politician from the shah’s era.
The news agency added that a former FBI agent, Robert Levinson, had disappeared in Iran in 2007 while working for the CIA on an unapproved intelligence mission.
The Washington Post said in a report that there had been no official US confirmation of the release.
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