They include pastor Saeed Abedini, in jail for three years after being convicted of undermining national security, and former US Marine Amir Hekmati, who is serving 10 years for cooperating with hostile governments.
The unnamed official was quoted by news agencies as saying a Swiss plane carrying the four left Tehran on January 17.
Yeganeh Salehi, Rezaian’s wife, was arrested along with her husband on July 22, 2014.
“We are relieved that this 545-day nightmare for Jason and his family is finally over”, says Fred Ryan, the newspaper’s publisher, in a statement.
A fifth American, Matthew Trevithick, was also released by Iran, though his release was not part of the negotiated prisoner swap.
“The US sanctions against Iran’s ballistic missile programme… have no legal or moral legitimacy”, Mr Ansari said in the televised news conference. Iran denied the charge.
He made no mention of a surprise prisoner exchange that also took place this weekend.
Obama said that although the Iran deal was never meant to resolve all problems between the USA and Iran, it had now created a window “to try to resolve important issues”.
Western media have named the Iranians as Nader Modanlo, Bahram Mechanic, Khosrow Afghahi, Arash Ghahreman, Tooraj Faridi, Nima Golestaneh, and Ali Saboonchi.
“As a result, the United States is imposing sanctions on individuals and companies working to advance Iran’s ballistic missile programme”.
Iran has successfully transferred some of its formerly frozen assets in order to ensure that financial sanctions have been fully lifted in accordance with a historic nuclear deal, the head of the central bank said on Tuesday.
Obama’s remarks came a day after the USA and European Union lifted global sanctions on Iran Saturday following the announcement of the worldwide Atomic Energy Agency that the country was complying with its nuclear-related obligations agreed last summer.