It is the company's first purchase in mainland Europe as it attempts to expand overseas.
Under the terms of the contract, BAA values the airport at between 67 billion and 80 billion lire (pounds 24m and pounds 29m) making BAA's investment worth between pounds 17m and pounds 20m.
Naples is the primary airport in southern Italy, handling about 2.9 million passengers each year. It is about the size of BAA's second-smallest airport, Edinburgh.
The move comes more than a year after BAA first signed a letter of intent with Gesac, the airport's operator to take a controlling equity stake. The contract still requires the approval of local authorities, which could take 70 days.