Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
The 22-year-old, who reportedly came close to joining Premier League club West Ham in July, becomes Rafael Benitez's latest addition at the Stadio San Paolo after the Azzurri coach persuaded Gonzalo Higuain, Dries Mertens, Jose Callejon and Raul Albiol to move to Naples.
Napoli posted a picture of Zapata signing his new contract alongside director of sport Riccardo Bigon on their official Twitter account, together with a message welcoming him to the Serie A club.
The former Colombia Under-20 international scored 14 goals in 30 appearances for Estudiantes after making a loan move from America de Cali permanent last year.