The EU foreign policy chief, Federica Mogherini, said the deal would contribute to improved regional and international peace and security, reports the BBC.
The landmark deal between Iran and world powers was agreed last July.
Lifting the sanctions will unfreeze billions of dollars of assets and allow Iran’s oil to be sold internationally.
The international nuclear watchdog, the IAEA, said its inspectors had verified that Tehran had taken the required steps.
As part of the deal, Iran had to drastically reduce its number of centrifuges and dismantle a heavy-water reactor near the town of Arak, both of which could be used in creating nuclear weapons.
Iran has always maintained its nuclear programme is peaceful, but opponents of the deal – such as some US Republicans – say it does not do enough to ensure the country cannot develop a nuclear bomb.
The US Secretary of State John Kerry has ordered that US nuclear-related economic sanctions against Iran be lifted.
Speaking in Vienna where he had been holding talks with his Iranian counterpart, Kerry said Iran had “undertaken significant steps” which many people “doubted would ever come to pass”.