The United States and Iran on Monday swapped five prisoners each in one of the arch-foes' first deals in years as Tehran gained access to $6 billion in frozen funds.

The five Americans freed by Iran, including one held for eight years, flew out of Tehran in a Qatari jet, hours after the unblocked funds were deposited in accounts also managed by Qatar.

The White House said it was "pleased to confirm" the plane carrying the freed Americans had left Doha, Qatar for the United States, and that President Joe Biden had spoken with the families of the Americans in an "emotional call".

The five had walked in the setting sun on the tarmac in Doha, three of them with arms around one another's shoulders.

One of them praised Biden for ignoring the political backlash and taking the "incredibly difficult decisions" that freed them.

"Thank you, President Biden, for ultimately putting the lives of American citizens above politics," Siamak Namazi, a businessman held since 2015, said in a statement.

Secretary of State Antony Blinken, who spoke to the released Americans by telephone after they landed in Doha, insisted the Biden administration had "no higher priority" than freeing US citizens.

"It's very good to be able to say that our fellow citizens are free," Blinken told reporters in New York, where he and Biden are taking part in UN meetings.

Two of the Iranian detainees arrived in Qatar, Iranian media said. The other three released by the United States have opted to remain there or in a third country.

After quiet discussions led in part by Qatar, the two countries completed the exchange after the transfer of $6 billion in funds, frozen by US ally South Korea.

The Biden administration has rejected criticism at home that it is paying "ransom," insisting the money will be used only humanitarian purposes, with a threat to re-freeze the funds if not.

But Iranian foreign ministry spokesman Nasser Kanani, speaking earlier in Tehran, said the clerical state will have "total access" to the assets.