Thursday's deal was initially announced in January 2016, after the sanctions against Iran were lifted, but was followed by regulatory delays.
Deliveries will begin in early 2017, it said. "So this agreement is also a significant first step in the overall modernization of Iran's commercial aviation sector".
The deal to buy 80 new aircraft was made possible by the Iran nuclear deal, which decreased sanctions on the Islamic Republic in exchange for a downgrade to its nuclear programs.
Following its competitor, Airbus Group SE (EPA:AIR) recently signed its deal with IranAir to sell around 100 commercial jets after its biggest rival Boeing Co.
Under the agreement, Airbus would deliver 46 single aisle A320 series commercial jets, 38 wide body A330 along with 16 more A350 long range wide body aircraft for global flight operations.
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The deals were made possible after the USA and other world powers agreed previous year to lift the sanctions on Iran in exchange for curbs on its nuclear activities.
"This is a landmark agreement not only because it paves the way for Iran Air's fleet renewal", said Fabrice Bregier, Airbus President and Chief Executive Officer, in a statement.
The Boeing planes will be delivered over a 10-year period, Parvaresh said.
As well as further modernizing Iran's aviation fleet, which has been hobbled by years of sanctions, the deal is a boon to Airbus too as Iran's flag carrier had finalized a deal for 80 jetliners from US plane maker Boeing Co.
Farhad Parvaresh, director and CEO of Iran Air, the national carrier taking conveyance of the planes, called the arrangement "the following conclusive stage" in the restoration of the aircraft's business armada.