The government will list 28 percent of the operator on the stock market and has agreed to sell another 21 percent to a core group of anchor investors, Pastor said. It will hold on to 51 percent of the firm.
Aena is the world's largest airport operator by passenger numbers, with nearly 196 million traveller arrivals or departures last year.
It runs 46 airports and two heliports in Spain and another 15 abroad, including London's Luton.
Aena was hit hard by Spain's economic downturn and underwent a massive overhaul which included job cuts and a rise in airport taxes to restore it back to financial health.
Deputy Prime Minister Soraya Sáenz de Santamaría said Aena's stock market listing was only possible thanks to "a deep transformation of the company which made it profitable".
Aena was initially scheduled to be listed in November but the operation had to be cancelled at the last moment after government officials discovered that there had not been a public tender for the role of auditor.