Some sanctions not linked to the nuclear deal will remain in place, including European sanctions relating to human rights
Iran's president has hailed the end of crippling economic sanctions on his country after the UN confirmed Tehran had drastically scaled down its nuclear programme.
Hassan Rouhani said Iranians had "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", according to state news agency IRNA.
He added: "We are a messenger of peace, stability and security in the region and the world."
The UN's nuclear watchdog, the International Atomic Energy Agency (IAEA), confirmed on Saturday that Iran fulfilled its side of last year's landmark nuclear deal with six world powers.
In return, the United States, European Union and United Nations have lifted a raft of nuclear-related sanctions.
The move will allow Iran to immediately recoup some $100bn (around €91bn) in assets frozen overseas.
US Secretary of State John Kerry said: "I hereby confirm that the International Atomic Energy Agency has verified that Iran has fully implemented its required commitments... The US sanctions-related commitments... are now in effect."
Meanwhile, in a joint news conference with Iran's Foreign Minister Javad Zarif, EU foreign policy chief Federica Mogherini said the accord "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".
The announcement came hours after the US and Iran reached an agreement on a prisoner swap, bringing an end to 14 months of negotiations.
Tehran confirmed that four inmates with dual Iranian-US nationality have been released from its jails, including Washington Post reporter Jason Rezaian.
US officials say a fifth American, student Matthew Trevithnick, has also been freed, but that his release was not part of the prisoner swap.
Seven Iranians, being held in prisons across the US, have been released in return.
Western powers imposed sanctions on Iran over fears it was planning to use its atomic programme to develop nuclear weapons, although Tehran always maintained its nuclear ambitions were peaceful.
It is thought that since 2012 the sanctions have cost Iran some €133bn in oil revenues alone.
Iran has the fourth biggest oil supplies in the world and the free flow of Iranian oil into the world market could mean lower prices at the pumps.
Some sanctions not linked to the nuclear deal will, however, remain in place, including European sanctions relating to human rights and US sanctions relating to terrorism.
Britain's Foreign Secretary Phillip Hammond said it would make the world a "safer place".
Others are alarmed at the prospect of closer Western ties with Shia Iran, including Sunni Saudi Arabia and Israel.
According to Israeli Prime Minister Benjamin Netanyahu, Iran "has not relinquished its ambition to obtain nuclear weapons, and continues to act to destabilise the Middle East and spread terror throughout the world".
Democratic presidential hopeful Hillary Clinton took credit for helping to start the sanctions pressure on Iran during her 2009-2013 tenure as Mr Obama's secretary of state.
But she also urged new sanctions on Tehran over its ballistic missile testing programme.