AENA said that it would begin a bidding process to contract a service provider in October.
The agency also said that it would quadruple the current speed of the internet.
"Offering free Internet access via Wi-Fi in airports is yet another step in Aena's commitment to the development of digital passenger services," AENA said in the announcement.
The Wi-Fi programme would be combined with an existing paid premium service for those who want even higher speeds.
Currently Kubi Wireless offers 30 minutes of free internet at 28 airports, including Adolfo Suárez Madrid-Barajas International Airport.