The legal acts have no immediate effect but cement a process that began with a deal reached in July to end sanctions against Iran in exchange for curbs on a program that the West suspected was aimed at developing a nuclear bomb.
For the waivers to come into force, Iran, which has always denied seeking nuclear weapons, must now demonstrate to the International Atomic Energy Agency (IAEA) that it has restricted its nuclear program as promised, a process that Western officials say is likely to take at least two months.
Sunday was "adoption day" for the agreement clinched in Vienna by Iran, the United States, Britain, France, Germany, Russia and China and endorsed 90 days ago by the United Nations.
The European Union formally enacted the legislative framework for lifting all nuclear-related economic and financial sanctions on Iran by publishing the documents on its official website.
In Washington, President Barack Obama directed the secretaries of state, treasury, commerce and energy to "take all necessary steps to give effect to the US commitments with respect to sanctions described in (the Iran deal)."
"Today marks an important milestone toward preventing Iran from obtaining a nuclear weapon and ensuring its nuclear program is exclusively peaceful going forward," he said in a statement.
Iran had passed a law on Oct. 14 approving the terms of the nuclear deal.
A range of restrictions have been imposed on Iran over several decades, dating back to 1979 when Iranian students stormed the US Embassy in Tehran. But it was the US and EU sanctions imposed in 2012, which targeted Iranian oil exports and international financial transactions, that inflicted most economic pain on Iran and its people.
Germany's foreign minister said the EU sanctions were likely to remain in place at least until January.
Implementation could take months
A senior Western diplomat based in Europe added: "Implementation can be expected to take place at the end of the year or the beginning of next year, but of course only once the IAEA has given the green light."
Last week, the IAEA said Iran had given it the information it needed to assess whether its past activities had anything to do with nuclear weapons, a condition that was part of the deal.
Separately, Iran told the IAEA on Sunday that it would fulfill its commitment to implement the Additional Protocol to its Comprehensive Safeguards Agreement, allowing UN inspectors more intrusive access to Iranian nuclear facilities.
Iran will adopt the protocol on "implementation day," the IAEA said in a statement.
Other steps that Iran must take to meet the requirements of the deal include reducing the number of uranium-enrichment centrifuges it has in operation and cutting its stockpile of enriched uranium.
US officials said the United States, China and Iran would release a joint statement on Sunday committing to the redesign and reconstruction of the Arak research reactor so that it does not produce plutonium, one of the most difficult parts of the nuclear deal.
Unilateral US sanctions against Iran that are not tied to its nuclear programme, such as those related to human rights, will remain even after the nuclear deal is implemented.
A United Nations embargo on conventional weapons will be lifted in five years, and a UN embargo on ballistic missiles in eight.
The US officials made clear that Iran's decision to test a ballistic missile a week ago in violation of the UN ban was not a breach of the nuclear deal, even though Washington has said the missile is capable of delivering a nuclear warhead.
Senior officials from the six world powers, Iran and the European Union will hold a first meeting in Vienna on Monday to monitor implementation of Iran's commitments, a Western diplomat said.