Three Iranian-Americans have left Tehran under a prisoner swap following the lifting of most international sanctions on Iran.
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 imposed the new sanctions after delaying the action for more than two weeks during tense negotiations to free five US prisoners, according to sources.
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," Barack 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 US official said a Swiss plane had left carrying Jason Rezaian, the Washington Post's Tehran bureau chief, Saeed Abedini, a pastor from Idaho and Amir Hekmati, a former Marine from Michigan, as well as some family members.
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 yesterday, 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 US administration official said.
Several Iranian-Americans held in US prisons after being charged or convicted for sanctions violations have also been released, their lawyers said.
Speaking to parliament, Mr 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 European Union, United States and UN have scrapped the sanctions in return for Tehran complying with the deal to curb its nuclear ambitions - ambitions that Tehran said were peaceful.
But Mr Rouhani noted bitter opposition to the lifting of economic curbs from Israel, some members of the US 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, Mr 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.
In The Hague, the US and Iran settled a longstanding claim, releasing to Tehran $400m in funds frozen since 1981 plus $1.3bn in interest, the US State Department said.
The funds were part of a trust fund once used by Iran to purchase military equipment from the US but which was tied up for decades in litigation at the Iran-US Claims Tribunal.
The settlement announcement was made after Tehran released the US detainees.
The nuclear deal has been widely welcomed across Europe.
Minister for Foreign Affairs Charlie Flanagan said: "I welcome the news that the International Atomic Energy Agency has verified the implementation of Iran's nuclear commitments under the Joint Comprehensive Plan of Action, in line with what was agreed last July.
"This is a critical landmark in the implementation of that agreement and EU sanctions will now be lifted.
"This agreement represents an important cooperative effort to deal with one source of tension in a region that already suffers from instability and conflict," added Mr Flanagan.