The move is seen as a key step towards lifting UN, EU and US sanctions.
The IAEA concluded that Iran conducted nuclear weapons-related research until 2003 and to a lesser extent until 2009, but found no evidence of this since.
The lifting of sanctions, agreed in a July deal with world powers, hinged on the IAEA's findings on the issue.
Iran has strongly denied pursuing a clandestine nuclear weapons programme.
Iranian Foreign Minister Javad Zarif welcomed Tuesday's announcement by the Vienna-based IAEA (International Atomic Energy Agency), saying it showed the peaceful nature of Iran's nuclear programme.
"This resolution goes far beyond closing the issue of so-called PMD (Possible Military Dimension) and cancels the 12 previous resolutions of the council of governors of the IAEA which seriously restricted our country's nuclear programme," Mr Zarif was quoted as saying by Iranian media.