WASHINGTON—New details of the $400 million U.S. payment to Iran earlier this year depict a tightly scripted exchange specifically timed to the release of several American prisoners held in Iran.

The picture emerged from accounts of U.S. officials and others briefed on the operation: U.S. officials wouldn’t let Iranians take control of the money until a Swiss Air Force plane carrying three freed Americans departed from Tehran on Jan. 17. Once that happened, an Iranian cargo plane was allowed to bring the cash home from a Geneva airport that day.

President Barack Obama and other U.S. officials have said the payment didn’t amount to ransom, because the U.S. owed the money to Iran as part of a longstanding dispute linked to a failed arms deal from the 1970s. U.S. officials have said that the prisoner release and cash transfer took place through two separate diplomatic channels.

But the handling of the payment and its connection to the Americans’ release have raised questions among lawmakers and administration critics.

The use of an Iranian cargo plane to move pallets filled with $400 million brings clarity to one of the mysteries surrounding the cash delivery to Iran first reported by The Wall Street Journal this month. Administration officials have refused to publicly disclose how and when the transfer took place. Executives from Iran’s flagship carrier, Iran Air, organized the flight from Tehran to Geneva where the cash—euros and Swiss francs and other currencies—was loaded onto the aircraft, these people said.