In a sign of sustained readiness to track Iranian compliance with remaining United Nations curbs, the United States imposed fresh sanctions on 11 companies and individuals for supplying Iran's ballistic missile programme.
The Obama administration had delayed the step for more than two weeks during tense negotiations to free five American prisoners, according to people familiar with the matter. Iran conducted a precision-guided ballistic missile test last October, violating a UN ban.
"This is a good day because once again we are seeing what's possible through strong American diplomacy," Obama said at the White House. "These things are a reminder of what we can achieve when we lead with strength and with wisdom."
Iranian President Hassan Rouhani hailed the nuclear deal as a "golden page" in Iran's history and said the agreement could be used as a model to resolve other regional issues.
The lifting of sanctions and the prisoner deal considerably reduce the hostility between Tehran and Washington that has shaped the Middle East since Iran's Islamic Revolution of 1979.
A Swiss plane took Jason Rezaian, the Washington Post's Tehran bureau chief, Saeed Abedini, a pastor from Idaho and Amir Hekmati, a former Marine from Flint, Michigan, as well as some family members from Tehran to Geneva, Switzerland.
They landed about 1700 (GMT) and a Swiss Foreign Ministry spokesman told Reuters they had left for a US military base in Germany shortly afterwards.
One more Iranian-American released under the same swap, Nosratollah Khosravi-Roodsari, was not aboard the aircraft. A fifth prisoner, American student Matthew Trevithick, was released separately on Saturday, a US official said.
"We can confirm that our detained US citizens have been released and that those who wished to depart Iran have left," a senior U.S. administration official said.
Several Iranian-Americans held in US prisons after being charged or convicted for sanctions violations have also been released, their lawyers told Reuters on Sunday.
MONTHS OF TALKS
The prisoner deal was the culmination of months of contacts, secret talks and legal manoeuvring which came close to falling apart on at least one occasion.
Speaking to parliament on Sunday, Rouhani, a pragmatist elected in 2013 on promises to end Iran's years of sanctions and isolation, said he looked forward to an economic future less dependent on oil exports.
These are nevertheless likely to jump now that the US, European Union and U.N. have scrapped the sanctions in return for Tehran complying with the deal to curb its nuclear ambitions - ambitions that Tehran says were peaceful.
But Rouhani noted bitter opposition to the lifting of economic curbs from Israel, some members of the U.S. Congress and what he called "warmongers" in the region - an apparent reference to some of Iran's Gulf Arab adversaries, not least Saudi Arabia.
Presenting the draft budget for the next Iranian fiscal year, which begins in March, Rouhani told parliament the deal was a "turning point" for the economy of Iran, a major oil producer which has been virtually shut out of international markets for the past five years.
He later said he expected 5% economic growth in the next Iranian fiscal year beginning in March and assured foreign investors of political and economic stability.
"The nuclear negotiations which succeeded by the guidance of the Supreme Leader and support of our nation, were truly a golden page in Iran's history," he said.
Tens of billions of dollars' worth of Iranian assets will now be unfrozen and global companies that have been barred from doing business there will be able to exploit a market hungry for everything from automobiles to airplane parts.
After the prisoners were freed, it was announced that the United States and Iran settled a longstanding claim, releasing to Tehran $US400 million ($NZ622 million) in funds frozen since 1981 plus $1.3 billion in interest, the State Department said. The funds were part of a trust fund once used by Iran to purchase military equipment from the United States, which was tied up for decades in litigation at the Iran-US Claims Tribunal in The Hague.
