President Obama has hailed a deal restricting Iran's nuclear programme as a "historic understanding" which, if implemented, will make the world safer.
The framework agreement, struck after intensive talks, aims to prevent Tehran making a nuclear weapon in exchange for phased sanction relief.
Iran and the six world powers involved must now finalise the deal.
Iranians have been celebrating in the streets but Israel says the deal threatens its survival.
"This will be a long-term deal, that addresses each path to a potential Iranian nuclear bomb," the US President said in a statement after the deal was announced.
"If Iran cheats, the world will know it," he said, adding that the agreement was based not on trust but on "unprecedented verification". He said that if the deal is finalised, "we will be able to resolve one of the greatest threats to our security, and to do so peacefully".
According to "parameters" of the agreement published by the US state department, Iran must reduce the number of its centrifuges that can be used to enrich uranium into a bomb by more than two-thirds.
It also has to redesign a power plant so it cannot produce weapons-grade plutonium, be subject to regular inspections, and agree not to enrich uranium over 3.67% - far less than is required to make a nuclear bomb - for at least 15 years.
"There's new state of the art technology that will be used," US Secretary of State John Kerry told the BBC. "We will have tracking of their uranium from the cradle to the grave."
The framework agreement was announced by the European Union and Iran after eight days of intense negotiations in the Swiss city of Lausanne.
Western powers have long distrusted Iran's assertions that its nuclear programme is peaceful.
The talks at Lausanne's Beau-Rivage Palace hotel between Iran and the so-called P5+1 - the US, UK, France, China and Russia plus Germany - continued beyond the original, self-imposed deadline of 31 March.
The Iranian foreign minister, Javid Zarif, called it a "win-win outcome", but warned: "We have taken a major step, but are still some way away from where we want to be."
The parties have set a deadline of 30 June to reach a comprehensive pact, but these negotiations are expected to be tougher than those that led to the framework agreement.
Even so, there was jubilation overnight on the streets of Tehran.
If the deal is implemented it should mean the eventual lifting of sanctions that have crippled the Iranian economy.
Unusually, the US president's speech was aired live on Iranian state television, with some Iranians taking selfies with Mr Obama as a backdrop.
There was anger though from Israel, whose leader Benjamin Netanyahu has been a vocal critic of Iran and told President Obama the deal threatened the survival of Israel.
The Israeli prime minister said it would "increase the risks of nuclear proliferation and the risks of a horrific war", according to his spokesman.
In the US, the deal has been criticised by members of Congress who want US lawmakers to have the right to review any final agreement.
US House Speaker John Boehner said the deal represented an "alarming departure" from Mr Obama's original goals and that Congress should review the deal before sanctions on Iran were lifted.
BBC
