In a televised speech from the White House, Trump announced the exit.
Trump's decision is historic and might have huge consequences for the US role in the Middle East, but it highlights a sobering reality: The US never fully implemented the nuclear deal, or Joint Comprehensive Plan of Action (JCPOA).
"Instead of preventing Iran's path to a nuclear bomb, it actually paved the way, since in a few years Iran will be able to enrich uranium on an industrial level", he said.
Because of these facts, I believe that the decision to put the JCPOA at risk without any Iranian violation of the deal is a serious mistake. All my friends want to leave Iran.
Mr Johnson, who met with Central Intelligence Agency director Mike Pompeo on his visit, said the deal is "working" at its core, and the USA and its allies should work to "fix the rest".
She added, "The nuclear deal with Iran is crucial for the security of the region, of Europe and of the entire world".
The UK's ambassador to the US, Sir Kim Darroch, says the Iran agreement was "a good deal" but efforts were ongoing to "find some language, produce some action that meets the president's concerns".
Macron had pleaded with Trump to remain in the deal.
Ernest Moniz, Obama's energy secretary and top Iran deal negotiator told Vox, "You could say it's a bad deal because it doesn't cover Hezbollah, and Syria, and Yemen, and missiles, and human rights but that's not what the agreement is".
Give Donald Trump Nobel Peace Prize
Asked if the meeting could still fall through, Trump acknowledged that it was all temporary until a deal was reached. Speaking in Rome, Ms Mogherini said: "I am particularly anxious by the announcement tonight of new sanctions".
US National Security Adviser John Bolton is reported as saying that European companies doing business with Iran will have to finish within six months or face US sanctions.
"Iran will never compromise on this agreement, and will abide by this agreement to the end. This includes actions under both our primary and secondary sanctions authorities", he added.
The 2015 deal - worked out between Iran and the United States, France, Germany, the UK, the EU, China, and Russian Federation - eased sanctions on Iran in exchange for Tehran limiting its nuclear programme.
In a joint statement released by French President Emmanuel Macron's office, French, German and British leaders regretted the USA decision.
Iran's supreme leader, Ayatollah Ali Khamenei, whose hostility towards Washington is the glue that holds together Iran's faction-ridden leadership, had said Iran would "shred" the deal if the USA pulled out.
Russian Federation said late Tuesday it was "deeply disappointed" by the US decision to pull out of the deal, and ready to work with other parties to keep it alive.
President Donald Trump on Tuesday announced that the United States would withdraw from the worldwide deal and restore sanctions on Iran, leaving the future of the agreement in doubt. Analysts say that up to 1 million barrels per day of Iranian crude is at stake.
Experts from the Washington-based Arms Control Association also denounced the decision.
"We know that standing firmly in support of the JPCOA with our North Atlantic Treaty Organisation allies and others is extremely important".
Ska Keller, co-leader of the Greens/EFA group, said, "Donald Trump's solo run is a unsafe game with fire". "Any nation that helps Iran in its quest for nuclear weapons could also be strongly sanctioned by the United States".