The Guardian Council's vote, while apparently not unanimous, marks a major victory for the administration of moderate President Hassan Rouhani, which has campaigned on easing tensions with the West.
But it comes as Iran's powerful Revolutionary Guard publicized images of an underground missile base and also has fired off a new long-range surface-to-surface rocket, showing hard-liners will remain a potent force within the Islamic Republic.
Iranian state television announced the decision by the Guardian Council, one of the top leadership bodies in Iran's cleric-ruled system. The 12-member council, half appointed by Iran's Supreme Leader Ayatollah Ali Khamenei and half by the country's judicial chief with parliament's approval, must sign off on all bills before they become law.
Some council "members raised objections to the bill and found it contrary to the constitution. There were debates," state television quoted Ebrahimian as saying.
More From This Section
"At the end, a majority of the council members voted that the parliamentary legislation is not against the constitution and Shariah law."
Hard-liners had hoped to stall the deal in order to weaken Rouhani's administration ahead of February's parliamentary elections.
But many in Iran applauded the final nuclear deal, struck July 14 in Vienna, as it lifts crippling economic sanctions in exchange for limits on the nuclear program.
Another 17 did not vote at all, while 40 lawmakers did not attend the session.
The council's decision marks the last approval needed before starting the deal, which came after nearly two years of negotiations between Iran and the United States, Britain, France, Russia, China and Germany.