Airbus reached the deal in January to sell Iran 118 aircraft but it required approval from the US Office of Foreign Assets Control because some of the planes' components are made in the United States.
"Airbus applied for two licenses and the first one was granted yesterday night," an Airbus spokesman said.
"We expect the second license to be granted in the coming weeks," the spokesman added.
The deal was initially valued at USD 25 billion but Iranian officials say it is worth nearer USD 10 billion.