It is estimated that sanctions imposed in 2012 have cost Iran some $145bn in oil revenues alone
Barack Obama has said a landmark nuclear deal has "cut off every single path Iran could use to build a bomb".
Speaking from the White House, the US President explained how 98% of Tehran's stockpile of enriched uranium had been shipped out of Iran - "meaning they do not have enough material for even one bomb".
Meanwhile, a new reactor which was capable of producing plutonium is now useless after its core was filled with concrete.
Mr Obama said all of this, coupled with the fact that inspectors now have complete access to Iran's facilities, means the world will know if the country attempts to renege on the historic agreement signed in Vienna on Saturday.
Despite the diplomatic breakthrough, which also led to the release of four Americans from Iranian prisons, the President said some fresh penalties will be enforced on individuals and organisations involved in Iran's ballistic missile programme.
The scheme poses "a significant threat to regional and global security", US officials have said - and although these sanctions were first mooted in December, diplomats held off on implementing them until the prisoner swap was assured.
Mr Obama warned reporters that "profound differences" remain with Iran over "destabilising activities" - but expressed hope the deal will help Iran and its people to forge new ties with the world.
Iran is already benefitting financially from the agreement, as foreign accounts holding $100bn have been unfrozen.
And on Sunday, $400m of cash which was frozen in 1981 - plus $1.3bn in interest accrued since - was returned to Tehran following a settlement with the US.
Earlier, there were celebrations in Tehran as residents expressed optimism about the future of the Iranian economy - with President Hassan Rouhani saying his country had "reached out to the world in a sign of friendliness" through the deal.
Britain's Foreign Secretary Phillip Hammond said it would make the world a "safer place".
But others are alarmed at the prospect of the West moving closer to Shia Iran, including Sunni Saudi Arabia and Israel.
Israeli Prime Minister Benjamin Netanyahu said Iran "has not relinquished its ambition to obtain nuclear weapons, and continues to act to destabilise the Middle East and spread terror throughout the world".
It is thought that, since 2012, the sanctions have cost Iran some $145bn in oil revenues alone.
Iran has the fourth biggest oil supplies in the world and the free flow of Iranian oil into the world market could mean lower prices at the pumps.