The state-run IRNA news agency said 50 Boeing 737s and 30 Boeing 777s would be delivered over the next decade, in the biggest agreement to be struck with an American company since the 1979 revolution and US Embassy takeover.
Boeing had no immediate comment.
In September, Washington granted permission to Boeing and its European competitor Airbus to sell billions of dollars' worth of aircraft to Iran. The US and other world powers agreed last year to lift crippling sanctions on Iran in exchange for it curbing its nuclear activities.
Iranian Transport Minister Abbas Akhoundi, who attended the signing ceremony, said it was a "historic" day for Iranian aviation and that the deal would create 8,000 jobs for Iranians.
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"The deal has a clear message for the world: we support peace and security as well as the growth of Iran based on a win-win policy," he was quoted as saying. "We hope that despite changes in the US administration, the country will remain loyal to its commitments."
Iran Air CEO Farhad Parvaresh said the first Boeing plane is expected to arrive in April.