The UN's atomic watchdog late yesterday confirmed that Iran had complied with its obligations under last summer's accord and the United States and European Union announced they were lifting the sanctions that have for years crippled the country's economy.
Western governments hailed the announcement as a milestone though some critics, including Israel, alleged that Tehran was still seeking to develop a nuclear weapon.
The announcement followed news of a prisoner swap between Iran and the United States that will include the release of Washington Post correspondent Jason Rezaian, in another sign of thawing relations between the longtime foes.
"We Iranians have reached out to the world... Have opened a new chapter in the relations of Iran with the world," the official IRNA news agency quoted Rouhani as saying.
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Iran is "not a threat to any government or nation". The agreement, he said, "is not a loss for any country".
Rouhani, who has promised that 2016 will be a "year of prosperity" for Iranians, was to give a press conference later today.
EU foreign policy chief Federica Mogherini, representing the six world powers, announced the lifting of "multilateral and national" sanctions in Vienna, saying the deal showed that intense diplomacy could resolve even "the most difficult issues".
The United States lifted a raft of sanctions, with Secretary of State John Kerry saying in Vienna: "The United States, our friends and allies in the Middle East, and the entire world are safer because the threat of the nuclear weapon has been reduced."
The nuclear deal will also open up business in the 79-million-strong country.
The Vienna agreement was nailed down after two years of rollercoaster negotiations following Rouhani's election.
The highly complex deal drew a line under a standoff dating back to 2002 marked by failed diplomatic initiatives, ever-tighter sanctions, defiant nuclear expansion by Iran and threats of military action.