The deal was passed with 161 votes in favor, 59 against and 13 abstentions, the official IRNA news agency said.
However, parliament insisted that international inspectors would have only limited access to military sites.
The agreement, struck in July, authorizes the lifting of sanctions in return for Iran curbing sensitive nuclear activities.
Iran insists that its nuclear program is entirely peaceful.
The deal between Iran and the so called P5 1 – the US, UK, France, China and Russia plus Germany – was achieved after 20 months of negotiations.
But it has come in for criticism from hardliners in both Iran and the US.
In September, Republicans in the US Congress attempted to overcome the deal by voting on a motion of disapproval.
Democrats, however, assembled enough votes to block the motion and handed US President Barack Obama a political success.
In Iran, conservative MPs criticized for suggesting they were blatantly trying to delay the deal President Hassan Rouhani.
Correspondents say Iran’s parliament has seen clashes that are angry within the deal.
Crucial areas of the atomic deal:
Uranium enrichment: Iran can operate 5,060 first generation centrifuges, configured to enrich uranium to 3.67%, a level well below that needed to make an atomic weapon.
Plutonium generation: Iran has consented to reconfigure its heavy water reactor at Arak, to ensure that it will simply make a small quantity of plutonium as a by-product of power generation, and will not construct any move heavy water reactors for 15 years.
Reviews: International screens will be able to perform an extensive plan of inspection of Iran’s atomic facilities.
Military dimensions that are possible: Iran will allow foreign inspectors to investigate the so called “potential military measurements” to its program by December. This ought to ascertain whether the state harbored military ambitions for the nuclear program, a claim it’s always strenuously denied.
Sanctions: All US and EU energy, economic and financial sanctions, and most UN sanctions, will be revoked on the day Iran shows it has complied with the principal portions of the offer.