The order follows a commitment inked in January when President Hassan Rouhani visited Paris in the wake of a deal between Western powers and Iran over its nuclear programme.
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, the European aircraft maker said in a statement.
Iran Air's CEO Farhad Parvaresh said the deal was "an important step towards a stronger international presence in civil aviation".
"We hope this success signals to the world that the commercial goals of Iran and its counterparts are better achieved with international cooperation and collaboration."
In another deal earlier this month, Iran Air finalised a contract to buy 80 planes from Airbus' US competitor Boeing.
Boeing said that contract -- Iran's first deal with a US aviation firm since the 1979 Islamic revolution -- was worth €15.5 billion.
With the incoming administration of US President-elect Donald Trump expected to take a tough line on Iran, and American lawmakers recently voting for renewed sanctions, Boeing emphasised the employment opportunities that the deal would create.