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NEW: Israel slams announcement, saying Iran still has ambitions of acquiring a nuclear weapon

"I thank God for this blessing," Iranian President tweets

Economic sanctions against Iran are lifted as IAEA announces compliance on nuclear deal

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Iran has completed the necessary steps in a deal to restrict its nuclear program, meaning international economic sanctions are lifted, Iran and international inspectors said.

“It is an important day for the international community. I congratulate all those who helped make it a reality,” Amano said.

Amano will travel to Iran on Sunday to meet with President Hassan Rouhani and his top nuclear official.

The milestone meant that Iran had joined the UK, United States, France, Germany, China, Russia and the European Union in “the field of peaceful users” of nuclear energy, said Federica Mogherini, chief of foreign affairs for the EU.

Obama signed an executive order lifting the U.S. economic sanctions on Iran, the White House announced Saturday.

Iran nuclear deal: What happens next

Kerry issued a statement confirming the IAEA had 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.

In an address to Iran’s parliament Sunday morning, Rouhani said that all the parties involved were satisfied with the deal, “with the exception of Zionists and warmongers … American hardliners and extremists.”

“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 one of the nations applauding the deal.

“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,” said Yair Lapid, a member of the Knesset.

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.

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‘Implementation Day’

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 Saturday 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.

Details of July’s Iran nuclear deal

Under the agreement, Iran is obliged to take steps to put it further away from developing a nuclear weapon while keeping a peaceful nuclear energy program.

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 deal what’s next

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.

Iran without sanctions: European firms ready to pounce

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.

Why U.S. businesses could lose big in Iran

CNNMoney’s Heather Long and Jim Boulden and CNN’s Ben Brumfield and Steve Almasy contributed to this report.