US President Barack Obama said that with the deal, "every pathway to a nuclear weapon is cut off" for Iran.
His Iranian counterpart, Hassan Rouhani, said it opened a "new chapter" in Iran's relations with the world.
Negotiations between Iran and six world powers - the US, UK, France, China, Russia and Germany - began in 2006.
The so-called P5+1 want Iran to scale back its sensitive nuclear activities to ensure that it cannot build a nuclear weapon.
Iran, which wants crippling international sanctions lifted, has always insisted that its nuclear work is peaceful.
In a televised address, Mr Obama said the deal would make the world "safer and more secure", and provided for a rigorous verification regime. "This deal is not built on trust - it is built on verification," he said.
Immediately afterwards, Mr Rouhani gave his own televised address, in which he said the prayers of Iranians had "come true".
He said the deal would lead to the removal of all sanctions, adding: "The sanctions regime was never successful, but at the same time it had affected people's lives.''
After 12 years, world powers had finally "recognised the nuclear activities of Iran", he said.
Analysis: Kevin Connolly, BBC Middle East correspondent
Iran's enemies remain of the view that the Iranians are hell-bent on acquiring nuclear weapons at some point and have merely agreed to a delay in return for a variety of short-term concessions.
There is a danger now that Saudi Arabia will feel that a nuclear-capable Shia state must be matched by a nuclear capability in the hands of the Sunni states too.
That brings the nightmare of a nuclear arms race in the Middle East a step closer.
Both Mr Rouhani and Iranian Foreign Minister Mohammad Javad Zarif referred to the dispute over Iran's nuclear programme as an "unnecessary crisis".
Earlier, EU foreign policy chief Federica Mogherini said the agreement was "a sign of hope for the entire world".
"It is a decision that can open the way to a new chapter in international relations," she said.
Mr Zarif said the deal was "not perfect for anybody'', but that it was the "best achievement possible that could be reached".
Mr Obama, who is trying to persuade a sceptical US Congress of the benefits, said it would oblige Iran to:
- remove two-thirds of installed centrifuges and store them under international supervision
- get rid of 98% of its enriched uranium
- accept that sanctions would be rapidly restored if the deal was violated
- permanently give the International Atomic Energy Agency (IAEA) access "where necessary when necessary"
Sanctions relief would be gradual, Mr Obama said, with an arms embargo remaining in place for five years and an embargo on missiles for eight years.
'Significant step forward'
Separately, the IAEA and Iran said they had signed a roadmap to resolve outstanding issues.
IAEA head Yukiya Amano told reporters in Vienna, Austria, that his organisation had signed a roadmap "for the clarification of past and present outstanding issues regarding Iran's nuclear programme".
He called the agreement a "significant step forward", saying it would allow the agency to "make an assessment of issues relating to possible military dimensions to Iran's nuclear programme by the end of 2015".
There has been stiff resistance to a deal from conservatives both in Iran and the US. The US Congress has 60 days in which to consider the deal, though Mr Obama said he would veto any attempt to block it.
Israel's government has also warned against an agreement.
Prime Minister Benjamin Netanyahu said it was a "historic mistake" that would provide Iran with "hundreds of billions of dollars with which it can fuel its terror machine and its expansion and aggression throughout the Middle East and across the globe".
Source BBC
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