The entry of investors into Aena would take place in two stages. The first phase will involve the sale of a 21% stake to selected investors chosen via a tender process.
Spain's Ministry of Public Works hopes to complete this in September.
The second phase will involve a public offering of 28% of Aena's share capital that will be open to minority investors.
It is expected that, if all goes according to plan, the new part-public, part-private Aena will be listed on the stock market in November 2014.
According to Manuel Vargas, Aena president, the firm is worth about €16 billion. Aena carries a debt of more than €11 billion.
Aena is the world's leading airport manager, moving 187.4 million passengers in 2013. The company runs 46 airports and two heliports in Spain and another 15 airports abroad, most in Mexico.
Spain's Government also approved the opening of the passenger rail-transportation sector, allowing a private operator to provide service on routes linking Madrid with the main cities on Spain's eastern coast under an initial seven-year contract.