Iran's President Hassan Rouhani, whose 2013 election helped launch the Herculean diplomatic effort towards the July 14 Vienna deal, yesterday said it was a "glorious victory" for the "patient nation of Iran."
"Implementation Day" for the accord came after the International Atomic Energy Agency said its "inspectors on the ground verified that Iran has carried out all measures" agreed under the agreement.
EU foreign policy chief Federica Mogherini, representing the six world powers, said that as a result "multilateral and national economic and financial sanctions related to Iran's nuclear programme are lifted".
"This achievement clearly demonstrates that with political will, perseverance, and through multilateral diplomacy, we can solve the most difficult issues," Mogherini said in Vienna in a joint statement with Iranian Foreign Minister Mohammad Javad Zarif.
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The announcement also followed news of a prisoner swap between Iran and the United States in another sign of thawing relations between the two foes since the agreement was struck.
The steps taken by Iran, combined with ultra-close IAEA inspections, extend to at least a year -- from a few months previously -- how long Iran would need to make one nuclear bomb's worth of fissile material.
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"Today... The United States, our friends and allies in the Middle East, and the entire world are safer because the threat of the nuclear weapon has been reduced," US Secretary of State John Kerry said in Vienna.
UN Secretary-General Ban Ki-moon said it was a "significant milestone that reflects the good faith effort by all parties to fulfil their agreed commitments."
German Foreign Minister Frank-Walter Steinmeier called the implementation of the nuclear deal "a historic success for diplomacy".
In what was hailed last July as a momentous diplomatic breakthrough, the Vienna agreement was nailed down after two years of rollercoaster negotiations following the moderate Rouhani's June 2013 election.
The highly complex deal drew a line under a standoff dating back to 2002 marked by failed diplomatic initiatives, ever-tighter sanctions, defiant nuclear expansion by Iran and threats of military action.
The five detainees to be freed by Iran included Washington Post correspondent Jason Rezaian and Saeed Abedini, a pastor from Idaho, a senior US official said yesterday.
In exchange Washington said it had granted clemency to seven Iranians, six of whom were dual US-Iranian citizens, and dropped charges against 14 more.
The agreement, heralded as US President Barack Obama's biggest major foreign policy triumph, has by no means been universally cheered, however.
Israeli Prime Minister Benjamin Netanyahu said yesterday that Iran "has not relinquished its ambition to obtain nuclear weapons, and continues to act to destabilise the Middle East and spread terror throughout the world".
"Today, the Obama administration will begin lifting economic sanctions on the world's leading state sponsor of terrorism," Republican House Speaker Paul Ryan said.
Sunni Saudi Arabia, Iran's other great regional rival, is also alarmed at the prospect of warmer US-Iran ties and of predominantly Shiite Iran, newly flush with oil revenues, increasing its influence.
Iran's imminent return to the oil market has also contributed to the sharp slide in the price of crude to 12-year lows of under USD 30 per barrel this week, putting Saudi Arabia's public finances under strain -- and meaning that Iran's oil bonanza will be less lucrative than it had hoped for.
The deal has more than a decade to run, which is likely to be a bumpy road, experts say, not least if more hardline governments take power in Tehran or Washington.
Iran "has kept its word, and we will continue to do the same. But we will also remain vigilant in verifying Iran's compliance every hour of every day in the years ahead," Kerry said.