The Nigerian authorities discovered the weapons, including rocket launchers and grenades, last month in containers labelled as building materials.
They had said they would report the seizure if it was shown that UN sanctions had been broken.
Iran said the weapons were the subject of a "misunderstanding", which had been cleared up.
Nigeria's foreign minister, Odein Ajumogobia, said: "Following preliminary investigations, our permanent mission in New York has reported the seizure and inspection of the arms shipment from Iran."
Iran's Foreign Minister Manouchehr Mottaki, who visited Nigeria last week, said: "A private company which had sold conventional defence weapons to another country in West Africa had transferred the shipment via Nigeria which raised some doubts with relevant officials."
He said an Iranian representative of the company in Nigeria "had offered explanations and I believe the misunderstanding has been cleared up".
The France-based shipping company CMA CGM which transported the shipment said it was hidden in containers labelled as building materials and attempts were made to send it to Gambia before the Nigerian police seized it.
Iran is under UN sanctions because of its nuclear programme and is banned Iran from supplying, selling or transferring arms. Tehran denies accusations that its programme is aimed at developing nuclear weapons.
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