The international sanctions were lifted after the International Atomic Energy Agency (IAEA) announced that Tehran has met its obligations it committed under the deal agreed between world powers and Iran last year.
"This is a significant milestone that reflects the good faith effort by all parties to fulfil their agreed commitments," Ban said in a statement.
He welcomed the achievement of Implementation Day under the Joint Comprehensive Plan of Action (JCPOA) between the E3+3 (France, Germany, the United Kingdom, the United States, Russia and China) and Iran.
The UN stands ready to support the implementation of the JCPOA in accordance with the relevant decisions of the Security Council, Ban said, adding that this achievement demonstrates that international proliferation concerns are best addressed through dialogue and patient diplomacy.
The Secretary-General voiced hope that "the success of this agreement contributes to greater regional and international cooperation for peace, security and stability in the region and beyond".
In a statement, the IAEA's Director General Yukiya Amano said "Implementation Day" paves the way to begin verifying and monitoring Iran's nuclear-related commitments under the agreement.
Ban also welcomed reports of the release of a number of Americans who had been detained in Iran, including a Washington Post journalist, and a number of Iranians held by the US.
"Following the pressure brought to bear by the US and the international community, Iran has taken real, observable action that quadruples Iran's breakout time - a result that seemed improbable as recently as two years ago when negotiations on the JCPOA began," said US Ambassador to the UN Samantha Power.
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