President Barack Obama welcomed the deal, saying it included “substantial limitations which will help prevent Iran from building a nuclear weapon”.
Iran agreed to give better access to inspectors and halt some of its work on uranium enrichment.
However, Iranian negotiators insisted they still had a right to nuclear power.
Tehran denies repeated claims by Western governments that it is seeking to develop nuclear weapons. It insists it must be allowed to enrich uranium to use in power stations.
After four days of negotiations, representatives of the so-called P5+1 group of nations – the US, the UK, Russia, China, France and Germany – reached an agreement with Iran in the early hours of Sunday.
The specifics of the deal have yet to be released, but negotiators indicated the broad outlines:
Secretary of State John Kerry said the agreement would make the region safer for its allies, including Israel.
However, the Israeli government criticized the deal and said Israel did not feel bound by it.
“This is a bad agreement that gives Iran what it wanted: the partial lifting of sanctions while maintaining an essential part of its nuclear programme,” said a statement issued by the office of Prime Minister Benjamin Netanyahu.
The Israeli comments came as it was revealed that the US and Iran had held a series of face-to-face talks over the past year that were kept secret even from their allies.
Iran’s Foreign Minister Mohammad Javad Zarif said it was an opportunity for the “removal of any doubts about the exclusively peaceful nature of Iran’s nuclear programme”.
Mohammad Javad Zarif insisted that Iran had not given up its right to enrich uranium.
“We believe that the current agreement, the current plan of action as we call it, in two distinct places has a very clear reference to the fact that Iranian enrichment programme will continue and will be a part of any agreement, now and in the future,” he said.
The US state department gave more details of the deal, insisting that most sanctions would remain in place.
Restrictions on Iran’s petrochemical exports and some other sectors would be suspended, bringing in $1.5 billion in revenue.
Barack Obama warned that if Iran fail to keep its commitments, “we will turn off the relief and ratchet up the pressure”.
This deal may be the most significant agreement between the world powers and Iran for a decade.
Negotiators had been working since Wednesday to reach an agreement that was acceptable to both sides.
As hopes of a deal grew stronger, foreign ministers of the P5+1 joined them in Geneva.
It only became clear that a breakthrough had been made in Geneva early on Sunday.
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