International Atomic Energy Agency chief Yukiya Amano was due to hold talks in Tehran Monday on ensuring Iran's continued compliance with a nuclear deal the US and Iranian presidents hailed as a historic breakthrough.

The UN's atomic watchdog said Amano would meet with President Hassan Rouhani and Ali Akbar Salehi, the head of Iran's Atomic Energy Organization, to discuss monitoring and verifying Iran's commitments under the agreement.

"A lot of work has gone into getting us here, and implementation of this agreement will require a similar effort," IAEA chief Amano said in a statement after the deal.

The IAEA confirmed late Saturday that Tehran had complied with its obligations under last summer's accord, leading the United States and the European Union to lift sanctions imposed over Iran's disputed nuclear programme that crippled its economy for a decade.

Rouhani, a moderate whose 2013 election victory helped launch a huge diplomatic effort toward the deal struck on July 14 in Vienna, said the implementation was a crucial moment for his country.

"We Iranians have reached out to the world... have opened a new chapter in the relations of Iran with the world," the official IRNA news agency quoted him as saying.

In Washington, President Barack Obama said the breakthrough was vindication of his contentious policy of engagement.

"We achieved this through diplomacy without resorting to another war in the Middle East," he said in an address to the nation.

But Obama also noted that "profound differences" with Tehran remained over its "destabilising activities".

In a sign of those differences, Washington announced it had decided to target the Islamic republic's ballistic missile programme with new measures.

Five Iranian nationals and a network of companies based in the United Arab Emirates and China were added to an American blacklist, the US Treasury announced.

The White House had threatened to impose the measures last month but withdrew them after Rouhani hit out at both their timing and intent. Missiles were not part of the nuclear agreement.

Asked before the new sanctions were announced how Iran would react to fresh measures against it, Rouhani on Sunday had said: "Any action will be met by a reaction."

- Freed Americans leave Iran -

The new sanctions came after four Iranian-Americans, including Washington Post reporter Jason Rezaian, were released in a prisoner swap with the United States.

The exchange involved Rezaian, Christian pastor Saeed Abedini, former US Marine Amir Hekmati and a fourth man, Nosratollah Khosravi-Roodsari.

"Today, Jason Rezaian, ... Saeed Abedini, and Amir Hekmati arrived in Germany, and soon they will be reunited with their families," Secretary of State John Kerry tweeted.

The three arrived at a US military base in Germany, after a brief stop in Geneva, a US official said.

Kerry also confirmed the release of the fourth Iranian-American freed in the prisoner swap, Nosratollah Khosravi-Roodsari, and American Matthew Trevithick, who was released in a separate process.

Washington Post publisher Frederick Ryan said: "We are relieved that this 545-day nightmare for Jason and his family is finally over."

Under the exchange, Washington said it had granted clemency to seven Iranians, six of whom were dual US-Iranian citizens, and dropped charges against 14 others.

Obama welcomed the Americans' release, saying: "When Americans are freed, that's something we can all celebrate."

Rouhani, who has promised that 2016 will be a "year of prosperity" for Iranians, said that following the lifting of sanctions Iran would seek foreign investment of $30-$50 billion annually, to dramatically spur growth to eight percent.

Iran can now increase its oil exports, long the lifeblood of its economy though Rouhani has moved away from relying on crude.

Brent crude briefly fell to fresh lows below $28 a barrel Monday, tumbling to $27.67 on fears of a worsening supply glut with Iranian exports returning to the market.

The nuclear deal will also open up business in the 79-million-strong country.

Kerry said the United States would repay Iran a $400 million debt and $1.3 billion in interest dating to the Islamic revolution.

- Rollercoaster negotiations -

The Vienna agreement was nailed down after two years of rollercoaster negotiations following Rouhani's election.

It 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 steps taken so far by Tehran 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.

They include slashing by two-thirds its uranium centrifuges, reducing its stockpile of uranium -- enough before the deal for several bombs -- and removing the core of its Arak reactor, which could have given Iran weapons-grade plutonium.

Iran has always denied wanting nuclear weapons, saying its activities are exclusively for peaceful purposes.

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