The United States has imposed fresh sanctions on 11 companies and individuals for supplying Iran's ballistic missile program.
The move follows the lifting of international nuclear sanctions against Iran.
Four American-Iranians have also been freed in a prisoner swap as part of the deal.
An historic day and a great victory for Iran.
That's how Iranian President Hassan Rouhani described the completion of a nuclear agreement with the west.
The deal led to the lifting of international sanctions against Iran in return for the Islamic Republic complying to curb its nuclear ambitions.
President Rouhani told parliament it's a turning point for his country's economy.
"Today is the day of the victory of the people of Iran on the political arena, the people of Iran proved that constructive interaction is true and is the right way. We can have interactions with the world that is in the interest of our people and definitely not to the detriment of others. So as of today it is clear that our country has a big power called the power of diplomacy."
The United States has hailed the success of the nuclear deal, saying it will make the world safer.
US President Barack Obama says world powers have cut off every path Iran had to a nuclear bomb, while inspectors in Iran will monitor key nuclear facilities at all times.
Mr Obama hopes it'll be the start of improved relations between Iran and the rest of the world.
"For decades your government's threats and actions to destabilise your region have isolated Iran from much of the world and now our governments are talking with one another. Following the nuclear deal, you -- especially young Iranians -- have the opportunity to begin building new ties with the world. We have a rare chance to pursue a new path -- a different, better future that delivers progress for both our peoples and the wider world. That's the opportunity before the Iranian people."
But Mr Obama admits differences still remain.
Following the announcement of the nuclear deal, the US confirmed it has imposed fresh sanctions on 11 companies and individuals in Iran, Hong Kong and the United Arab Emirates for violating a United Nations ban on ballistic missile tests.
The fresh sanctions mean they can't use the US banking system, and financial institutions and companies are barred from dealing with them.
Meanwhile, Iran announced the release of five American-Iranians as part of a prisoner swap with the US.
President Obama it's all an example of what diplomacy can achieve.
"But today's progress -- Americans coming home, an Iran that has rolled back its nuclear program and accepted unprecedented monitoring of that program -- these things are a reminder of what we can achieve when we lead with strength and with wisdom; with courage and resolve and patience."
United Nations Secretary-General Ban Ki-moon has commended the moves.
"I am also heartened by the lifting of sanctions against Iran. I hope that the parties now move to fully carry out joint comprehensive plansof action in good faith. Now is the moment to push for cooperation on other pressing challenges through dialogue which should continue to guide a way forward for a safer future."
However, Israel continues to express its scepticism over the Iran nuclear agreement.
Prime Minister Binyamin Netanyahu says Israel will continue to monitor Iran for any violations.
Briefing his cabinet on Sunday, Mr Netanyahu called for harsh, aggressive sanctions for any violation by Iran.
"Were it not for our efforts to spearhead the sanctions and foil Iran's nuclear program, Iran would have already had nuclear weapons long ago. Israel's policy was and remained exactly the same: to not let Iran achieve nuclear weapons. It is clear that from now on Iran will have more means to use for its terror and aggression activity in the region and in the world. And Israel is ready to cope with any threat."
The European Commission says it will explore energy ties with Iran following the lifting of international sanctions, beginning in February.
The European Union executive is particularly keen to develop Iranian supplies as an alternative to Russia, whose powerful role as a source of around a third of EU oil and gas has divided the bloc.