The aircraft is powered by CFM International CFM56 engines and is one of 46 A320-family jets featured in the order, flightglobal.com reported.
Speaking at the handover event in Toulouse, France, Iran Air Chief Executive Farhad Parvaresh said: "Today is a memorable day for civil aviation in Iran."
He referred to a 'change in international perspective' which had helped to lay foundations for the agreement.
Parvaresh said that the 'distance' caused by 'biased political' adversity had been 'narrowed' by international peacemakers. "I can foresee great success and dignity for both of our companies," he added.
Airbus commercial aircraft president Fabrice Bregier said the delivery fulfilled a 'long-held ambition' to see a new Airbus flying in Iran Air colors.
"This agreement is one of the most significant deals in the history of civil aviation," he added at the ceremony.
Bregier told Parvaresh that he had an "opportunity to create an enormous legacy" for Iran, with new routes and greater accessibility to air transport — for which the A321 would serve as the 'perfect springboard'.