Prime Minister David Cameron has hailed the international community's deal with Iran as "historic", saying it will "keep Iran from developing a nuclear weapon and help to make our world a safer place".
US president Barack Obama heralded the nuclear deal with Iran as an opportunity that should be seized by the US.
Speaking at the White House, Obama said that every pathway for Iran to get a nuclear weapon was cut off under the agreement.
He also appeared to issue a warning to the Republicans in the US Congress sceptical of the White House's overtures to Iran, saying he would veto any any legislation that prevents the implementation of the nuclear deal.
He said it would be irresponsible to "walk away" from the deal, adding that the deal was a chance to move in a new direction.
"We should seize it," he said.
Federica Mogherini, the EU's foreign policy chief, has formally announced the Iranian nuclear agreement, a deal intended to end a dispute that has lasted more than a decade.
"It is a great honor for us to announce that we have reached an agreement on the Iranian nuclear issue," Mogherini said. "This is an historic day ... because we have created the conditions for building trust and opening a new chapter in our relationship."
"This is the end of our negotiations," she said. "But it is not the end of our common work."
Under the 'joint comprehensive plan of action' Iran has said it will not to seek or develop nuclear weapons, according to Mogherini.
She announced the deal alongside Mohammad Javad Zarif, the Iranian foreign minister.
Vladimir Putin, Russia's president, has welcome the nuclear deal with Iran, saying that with the deal signed "the world can breathe a sigh of relief".
The deal will see an easing of sanctions on Iran, including a UN arms embargo and ban on Tehran's ballistic missile programme, an advantage to Russia which is keen to sell arms to Iran.
Sergei Lavrov, Russia's foreign minister who has been involved in the nuclear talks, said that after the deal arms deliveries to Tehran would be possible if approved by the UN Security Council.
He also said Russia was counting on the United States carrying out a promise, which he said it had made in 2009, not to deploy missile defence systems in Europe once a nuclear deal was reached with Iran.,
Iran is to return to the global oil market with maximum capacity once sanctions against it are lifted, a deputy oil minister has been quoted as saying.
The relaxing of sanctions will be part of the historic nuclear deal agreed today in Vienna.
"We will try to maximise our crude export capacity to Europe and restore 42 to 43 percent share in the European market before the sanctions were imposed," Mohsen Qamsari, director of international affairs at the National Iranian Oil Company was cited by the Shana news agency as saying.
Meanwhile the Iranian cabinet is set to meet Supreme Leader Ayatollah Ali Khamenei on Tuesday, according to the Tasnim news agency, following the nuclear deal.
"The cabinet will meet the Supreme Leader tonight," Tasnim quoted Parviz Esmaeili, an official in charge of communications and information at the presidential office, as saying.
Iran will be allowed to conduct research and development (R&D) with uranium for advanced centrifuges during the first 10 years of the nuclear agreement with major powers, according to the text of the deal posted on the Russian foreign ministry website.
"Iran will continue to conduct enrichment R&D in a manner that does not accumulate enriched uranium," the text of the agreement said.
"For 10 years and consistent with its enrichment R&D plan, Iran's enrichment R&D with uranium will only include IR-4, IR-5, IR-6 and IR-8 centrifuges.
"Mechanical testing on up to two single centrifuges for each type will be carried out only on the IR-2m, IR-4, IR-5, IR-6, IR-6s, IR-7 and IR-8."
Meanwhile, a senior Iranian oil official said that several refineries have expressed willingness to buy Iranian oil, according to Iran's Shana news agency.
The Iranian president has tweeted images of the signing of an agreement between Iran and the UN nuclear watchdog.
The images were tweeted on Hassan Rouhani's English language account.
Yukiya Amano, who heads the International Atomic Energy Agency (IAEA), announced the road map agreement earlier, saying it would allow for outstanding questions the agency has on Iran's nuclear programme to be resolved by the end of the year.
Rouhani also confirmed the Iran nuclear deal, saying it showed that "constructive engagement works".
The UN's nuclear watchdog has agreed a road map with Iran that should allow for outstanding questions it has on Iran's nuclear programme to be resolved by the end of the year.
Yukiya Amano, who heads the International Atomic Energy Agency (IAEA), said the road map "provides for technical expert meetings, technical measures and discussions, as well as some separate agreements regarding the issue of Parchin".
Parchin is an Iranian military site which the agency has repeatedly sought to access.
"By 15 December 2015, the Director General will provide ... the final assessment on the resolution of all past and present outstanding issues," he said.
Israel's prime minister has called the Iran nuclear deal a "mistake of historic proportions" and indicated Israel will try to block Iran's nuclear ambitions.
"Iran is going to receive a sure path to nuclear weapons. Many of the restrictions that were supposed to prevent it from getting there will be lifted," Netanyahu said at the start of a meeting with Bert Koenders, the Dutch foreign minister, in Jerusalem.
"Iran will get a jackpot, a cash bonanza of hundreds of billions of dollars, which will enable it to continue to pursue its aggression and terror in the region and in the world. This is a bad mistake of historic proportions."