"Relations between Iran and the IAEA now enter a new phase. It is an important day for the international community. I congratulate all those who helped make it a reality," said Director General Yukiyo Amano of the International Atomic Energy Agency.
Amano will travel to Iran on Sunday to meet with President Hassan Rouhani and his top nuclear official.
European Union Foreign Affairs Chief Federica Mogherini said that the economic sanctions against Iran were lifted now that the country has joined the UK, United States, France, Germany, China, Russia and the EU in "the field of peaceful users" of nuclear energy.
President Barack Obama signed an executive order lifting some of the U.S. economic sanctions on Iran, the White House announced.
Secretary of State John Kerry issued a statement confirming the IAEA has verified that Iran "has fully implemented its required commitments."
"Iran has undertaken significant steps that many, and I do mean many, people doubted would ever come to pass. And that should be recognized, even though the full measure of this achievement can only be realized by assuring continued full compliance in the coming years," Kerry said.
Kerry called the world a safer place because of the developments.
"Today marks the moment that the Iran nuclear agreement transitions from an ambitious set of promises on paper to measurable action in progress. Today, as a result of the actions taken since last July, 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," Kerry said.
UK Foreign Secretary Philip Hammond echoed Kerry's comment, saying the deal "makes the Middle East and the wider world a safer place." He added that Iran's nuclear program has been substantially rolled back.
Rouhani welcomed the IAEA announcement.
"Implementation Day -- I thank God for this blessing & bow to the greatness of the patient nation of Iran. Congrats on this glorious victory!" Rouhani said via Twitter.
French Foreign Minister Laurent Fabius called Saturday's news "an important step for peace and security."
Israel was not happy.
"Today, a country that threatens the existence of Israel, denies the Holocaust, destabilizes the Middle East, subjugates its own people and supports terror across the globe is being strengthened by the international community," Yair Lapid, a member of the Knesset, said. "The lifting of sanctions strengthens Hezbollah, it strengthens (Syrian President Bashar al-) Assad, it strengthens terrorists across the region who benefit from Iranian support."
Prime Minister Benjamin Netanyahu said Israel is monitoring Iran and will report any violation of the nuclear agreement. Iran has not given up on its ambition to acquire a nuclear weapon, he said.
Iran's foreign minister arrived in Vienna saying he was confident the U.N.'s nuclear watchdog would certify that his country was complying with the terms of a deal to restrict its nuclear program in exchange for the lifting of some international economic sanctions.
The IAEA -- the U.N. nuclear watchdog organization -- released its report assessing Iran's compliance with an agreement with foreign powers, including the United States and the European Union.
Many observers expected the IAEA would corroborate Iranian compliance.
The release heralds "Implementation Day," the formal name for the start of the next phase in the agreement called the Joint Comprehensive Plan of Action, which was hammered out with Iran in July
. The new "Day" will mean the first wave of economic relief for Iran.
Before the announcement, Iranian Foreign Minister Mohammad Javad Zarif had already exuded confidence in a post to Twitter shortly after arriving in Vienna that the milestone has been met. "#ImplementationDay, it's now time for all -- especially Muslim nations -- to join hands and rid the world of violent extremism. Iran is ready."
Zarif continued his exuberance in a subsequent posting later in the day.
"We're getting to #ImplementationDay. Nothing serious. Diplomacy requires patience, but we all know that it sure beats the alternatives," he said on Twitter.
Under the agreement, in exchange for lifting sanctions Iran is obliged to take steps to put it further away from developing a nuclear weapon while keeping a peaceful nuclear energy program.
In a possible sign of the thaw in relations, it was announced that Iran had freed four American prisoners,
including Washington Post journalist Jason Rezaian, as part of a prisoner swap deal, according to Iran's semi-official FARS news agency, which quoted the Tehran prosecutor. Another American, who was not a part of the exchange, also was released.
Iran has various obligations under the nuclear agreement.
It must reduce its level of uranium enrichment, dramatically reduce the size of its stockpile of enriched uranium, reduce the number of centrifuges, and agree to unfettered international inspections.
But not all nuclear-related sanctions will be rescinded immediately -- that won't happen for about 10 years, should the deal hold. But this month's milestone will mean Iran will be able to sell its oil again on world markets
and its banks will be able to connect to the global system.