The deal, which was agreed last November in talks with world powers, envisages easing of some international sanctions on Tehran.
US President Obama said more work is required to strike a long-term deal
In an announcement, the EU's foreign policy chief Catherine Ashton, representing the five permanent members of the UN Security Council - US, Russia, China, France and Britain - plus Germany in the talks with Iran, said that the world powers would now ask the IAEA or, the UN's nuclear watchdog to verify the deal is implemented.
"We will ask the IAEA to undertake the necessary nuclear-related monitoring and verification activities," she said.
Meanwhile, welcoming the news, US President Barack Obama said more work was required to strike a long-term deal and warned of new sanctions in case there was a breach.
"Beginning 20 January, Iran will for the first time start eliminating its stockpile of higher levels of enriched uranium and dismantling some of the infrastructure that makes such enrichment possible."
In return, Obama said, over the next six months the US and the other five powers would begin to implement "modest relief" so long as Iran fulfilled its obligations.
While curtailing its nuclear programme, Iran will now permit more intrusive inspections beginning Jan 20 under the terms of an agreement reached with world powers.
Tehran, under the terms of the deal, has agreed to halt its enrichment of uranium above 5 percent purity, "neutralise" its stockpile of near-20 percent-enriched uranium while offering daily access to inspectors.
In return, the world powers agreed to suspend certain trade related sanctions in gold and precious metals, Iran's automotive sector, and its petrochemical exports.
On Nov 24, Iran and the six world powers had reached an initial accord in Geneva that had not taken effect.
The West accuses Iran of seeking nuclear weapons, but the Islamic republic has consistently denied that.