Abbas Akhoundi, quoted by Iranian media, said the deal "will be signed between Iran Air and Airbus" when Rouhani is in Paris on Wednesday as part of his first official European visit.
Rouhani's trip follows the implementation of a nuclear deal with world powers that curbs Tehran's atomic activities in exchange for the lifting of punishing economic sanctions.
Iran desperately needs to modernise its ageing passenger fleet, which has only 150 operational planes out of more than 250, according to Akhoundi.
"We have been negotiating for 10 months" for the purchase of planes but "there was no way to pay for them because of banking sanctions," Iranian state media quoted Akhoundi as saying.
"We need 400 long- and mid-range and 100 short-range planes," he added.
The first batch of new planes will arrive in the country by March 19, he said.
Iran, with a population 79 million, has a good road network but still needs major transport upgrades, which Tehran hopes will aid tourism.
Rouhani is to visit Italy and France on January 25-27 to boost Iran's economic ties with Europe.
Iran currently has no deals in place with American manufacturer Boeing "because of problems with negotiating with the US," according to Akhoundi.
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State television said the US Treasury had not yet permitted Boeing to enter talks with Iran, "but we will definitely negotiate with this company too," the minister added.
Apart from new planes, Iran's airports also need $250 million (230 million euros) worth of upgrades, he said.
Only nine of Iran's 67 airports are currently operational.
News of the Airbus deal came as aviation representatives from 85 companies met in Tehran on Sunday to assess ways to do business in the Islamic republic after sanctions were removed.
The CAPA 2016 Iran Aviation Summit was attended by 160 officials from the aerospace and travel industries, conference secretary Ahmad Reza Bayati told the official IRNA news agency.
International flights to and from Iran have already increased by 10 percent since March, the start of Iranian calendar, as the country is well-positioned on many transcontinental air routes, Bayati said.
While new planes will be bought by state-owned Iran Air, the country hopes private airlines can rent serviceable planes from major companies in Europe.
Akhoundi said the government would support any company willing to buy new planes.
Iran has also stopped controlling ticket prices to allow more competition in the private sector.
The Islamic republic on Saturday signed a $2 billion contract with China to electrify the railway line linking Tehran with second city Mashhad, Akhoundi said.