Iran "has opened a new chapter" in its ties with the world, President Hassan Rouhani said, hours after international nuclear sanctions were lifted.
The move came after the international nuclear watchdog, the IAEA, said Iran had complied with a deal designed to prevent it developing nuclear weapons.
Most Western governments hailed the move but Israel accused Tehran of still seeking to build a nuclear bomb.
Four dual US-Iran nationals were released from jail by Iran on Saturday.
They include Washington Post reporter Jason Rezaian, who was arrested in 2014 and jailed in November for espionage.
Early reports said all four had left the country, however unnamed US officials later said that while "those who wished to depart Iran have left" and that one of the four, Nosratollah Khosravi-Roodsari, was not on the plane headed for Switzerland.
A fifth American, Matthew Trevithick, was also been released separately.
The US offered clemency to seven Iranians being held in the US for sanctions violations.
What are the sanctions?
Nuclear sanctions have been in place since 2006, on top of other sanctions stretching back decades:
- The economic sanctions being lifted now were imposed progressively by the US, EU and UN in response to Iran's nuclear programme
- The EU is lifting restrictions on trade, shipping and insurance in full
- The US is suspending, not terminating, its nuclear-related sanctions; crucially, Iran can now reconnect to the global banking system
- The UN is lifting sanctions related to defence and nuclear technology sales, as well as an asset freeze on key individuals and companies
- Non-nuclear US economic sanctions remain in place, notably the ban on US citizens and companies trading with Iran, and US and EU sanctions on Iranians accused of sponsoring terrorism remain in place
A flurry of Iranian economic activity is anticipated:
- Nearly $100bn (£70bn) of Iranian assets are being unlocked
- Iran is expected to increase its daily export of 1.1m barrels of crude oil by 500,000 shortly, and a further 500,000 thereafter
- Iran is reportedly poised to buy 114 new passenger planes from the Airbus consortium
UN, US and EU sanctions have hit Iran hard for years.
Mr Rouhani said everyone was happy with the deal, apart from those he described as warmongers in the region - Israel and hardliners in the US Congress.
"We Iranians have reached out to the world in a sign of friendliness, and leaving behind the enmities, suspicions and plots, have opened a new chapter in the relations of Iran with the world," he said in a statement on Sunday morning.
The lifting of sanctions was "a turning point" for Iran's economy, he added, saying the country needed to be less reliant on oil revenues.
US Secretary of State John Kerry, an architect of the deal, said it had been pursued "with the firm belief that exhausting diplomacy before choosing war is an imperative. And we believe that today marks the benefits of that choice".
However US Republican House Speaker Paul Ryan said the Obama administration had moved to lift economic sanctions "on the world's leading state sponsor of terrorism".
And Israel's Prime Minister Benjamin Netanyahu said: "Without an appropriate reaction to every violation, Iran will realise it can continue to develop nuclear weapons, destabilise the region and spread terror."
'Expectations are high' - Amir Paivar, BBC Persian business reporter
Iranian President Hassan Rouhani says the lifting of sanctions is a victory for the Iranian nation. It is one for him too.
Mr Rouhani had pledged to strike a deal ending the nuclear standoff. He just delivered his biggest promise. This will boost his allies in parliamentary elections next month.
But hardliners will not sit and watch. They call the shots in domestic, security and cultural areas. There is always danger of a backlash unless Mr Rouhani's faction shares the post-sanctions financial benefits with them.
Expectations are high, and managing them will be a difficult job. The impact of lifting of sanctions in livelihoods of many Iranian will not come overnight. Rouhani now says he will focus on boosting foreign direct investment and Iran's non-oil exports. Easier said than done.
The prospect of Iran doubling its crude oil exports has contributed to the continuing fall in the oil price. Benchmark Brent crude closed below $29 (£20.3) on Friday. Share prices in Saudi Arabia, the Arab world's largest stock market, fell more than 6% following the lifting of sanctions.
The IAEA said it had installed a device at the Natanz plant to monitor Iran's uranium enrichment activities in real time, in order to verify that uranium enrichment levels were kept at up to 3.67% as agreed in the deal with world powers.
As part of the deal, Iran had to drastically reduce its number of centrifuges and dismantle a heavy-water reactor near the town of Arak, both of which could be used in creating nuclear weapons.
Iran has always maintained its nuclear programme is peaceful, but opponents of the deal say it does not do enough to ensure the country cannot develop a nuclear bomb.