The delivery of an A321 is the first in a batch of 100 jets purchased by Iran Air to renew its aged passenger fleet, the report said.
According to Iran's official IRNA news agency, the A321 has already left France and will arrive in Iran shortly.
"Today, for civil aviation in Iran, is a memorable day," Iran Air Chief Executive Farhad Parvaresh said in France's Toulouse at the handover event on Wednesday.
"The change in international perspective" helped to lay foundations for the deal, Parvaresh said, hailing the agreement as "one of the most significant deals in the history of civil aviation."
This would be Iran's first brand-new plane in over 37 years. The country's current fleet is comprised of planes purchased before the 1979 Islamic revolution. All post-1979 purchases that were made with a variety of providers involved second-hand planes.
In December, Iran sealed a contract with Airbus to buy 100 aircraft worth over 18 billion U.S. dollars.
Parvaresh said that Iran Air would receive seven or eight planes from Airbus in 2017. He hoped that the delivery would be made in due time.
In January 2016, Iran signed a preliminary agreement with Airbus to purchase 106 commercial planes, however, the agreement waited for the U.S. Treasury Department's go-ahead license which was issued in November.
Also in December, Iran Air finalized another agreement with the U.S. Boeing to purchase 80 commercial planes.
The agreement, signed in capital Tehran, envisages the purchase of 50 twinjet narrow-body Boeing 737 planes and 30 long-range wide-body 777 aircraft with a total value of 16.6 billion dollars.
The planes by Boeing would be delivered to Iran within 10 years, Parvaresh said, adding that the first deliveries are expected in 2018.