"This aircraft has received its certificate of registration and an Iran Air team is in place to take delivery of it," the airline's chief executive officer, Farhad Parvaresh, told the Fars news agency.
"We hope to take delivery between now and the end of the week."
Iran Air completed the huge deal for 100 Airbus planes with a list price of around USD 20 billion (19 billion euros) on December 22.
But it required approval from Washington as some parts are manufactured in the United States.
The jets will bolster Iran's ageing passenger fleet with the addition of 46 A320 planes for medium-haul routes, 38 long-haul A330s and 16 A350s.
In another deal last month, Iran Air finalised an order for 80 planes from Airbus's US competitor Boeing.
Boeing said that contract -- Iran's first deal with a US aviation firm since the 1979 Islamic revolution -- was worth USD 16.6 billion.
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