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 reached after 20 months of negotiations.
But it has come in for criticism from hardliners in both the US and Iran.
In September, Republicans in the US Congress tried to sink the deal by voting on a motion of disapproval.
Democrats, however, gathered enough votes to block the motion and handed US President Barack Obama a political victory.
In Iran, conservative MPs criticized President Hassan Rouhani for suggesting they were deliberately trying to delay the deal.
Correspondents say Iran's parliament has seen angry clashes over the agreement.
Key areas of the nuclear 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. It can also operate up to 1,000 centrifuges at its mountain facility at Fordow - but these cannot be used to enrich uranium.
Plutonium production: Iran has agreed to reconfigure its heavy water reactor at Arak, so that it will only produce a tiny amount of plutonium as a by-product of power generation, and will not build any move heavy water reactors for 15 years.
Inspections: International monitors will be able to carry out a comprehensive program of inspection of Iran's nuclear facilities.
Possible military dimensions: Iran will allow foreign inspectors to investigate the so-called "possible military dimensions" to its program by December. This should determine whether the country ever harbored military ambitions for its nuclear program, a claim it has always strenuously denied.
Sanctions: All EU and US energy, economic and financial sanctions, and most UN sanctions, will be lifted on the day Iran shows it has complied with the main parts of the deal.
Courtesy BBC