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International sanctions on Iran were lifted Saturday after the United Nations nuclear agency declared Tehran had fulfilled its commitment to scale back its nuclear program.

"We have achieved a critical and auspicious milestone," Secretary of State John Kerry said at a press conference Saturday. "Iran has undertaken significant steps that many — and I do mean many — people doubted would ever come to pass."

The International Atomic Energy Agency verified Saturday that Iran was in full compliance, triggering the removal of the harsh sanctions imposed by the United Nations, United States and European Union.

The sanctions have cut off a nation of nearly 80 million people from the global financial system, drastically reduced the exports of a major oil producer and imposed severe economic hardship on ordinary Iranians. Most will be lifted immediately.

"This achievement clearly demonstrates that with political will, perseverance, and through multilateral diplomacy, we can solve the most difficult issues and find practical solutions that are effectively implemented," EU High Representative Federica Mogherini and Iranian Foreign Minister Javad Zarif said in a joint statement.

Related: Iran Frees Long-Held Washington Post Reporter Jason Rezaian

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The lifting of the sanctions came just hours after five Americans were released from Iranian prison, including Washington Post Reporter Jason Rezaian, 39, who had been held for more than 500 days.

The two diplomatic achievements "were not directly related," Kerry said. But he added that "there is no question that the peace and the progress of the humanitarian talks accelerated in light of the relationships forged and the diplomatic challenges unlocked in light of the nuclear talks."

Senior administration officials echoed that the nuclear deal allowed easier access to focus on the release of the Americans, but only recently was it clear that they would be released on the same day that the sanctions were dropped.

"We will also remain vigilant in verifying Iran's compliance."

The Jan. 16, 2016, "implementation day" of the nuclear deal agreed upon last year marks the biggest re-entry of a former pariah state onto the global economic stage since the end of the Cold War, and a turning point in the hostility between Iran and the United States that has shaped the Middle East since 1979.

It is a defining initiative for both President Barack Obama and Iran's President Hassan Rouhani, both of whom faced strong opposition from hardliners at home in countries that have called each other "Great Satan" and part of the "axis of evil."

U.K. Foreign Secretary Philip Hammond hailed the implementation of the nuclear agreement.

"The nuclear deal with Iran, in which Britain played a major role, makes the Middle East and the wider world a safer place," Hammond said in a statement. "Iran's nuclear program has been substantially rolled back," he said.

Related: Meet The Americans Freed From Iranian Prison

Under the deal, Iran agreed to forego enrichment of uranium, which world powers feared could be used to make a nuclear weapon. Kerry said Iran's current stockpile is 2 percent of what it was before the agreement, and said the country has removed two-thirds of its centrifuges.

Senior administration officials said Iran had shipped away 45,000 pounds of enriched nuclear material and completely ceased nuclear enrichment activities.

But, Kerry acknowledged, "this marker alone does not wipe away all the concerns that the international community has rightly expressed about Iran."

"We will ... remain vigilant in verifying Iran's compliance," he said.

With sanctions lifted, Iran plans to swiftly ramp up its exports of oil. Global companies that have been barred from doing business there will be able to exploit a hungry market for anything from automobiles to airplane parts.

"We also know without a doubt that there is not a challenge in the entire region that couldn't become much more complicated, much worse, if Iran had a nuclear weapon. And that is why this agreement is so important," Kerry said.