The midfielder arrives at the Giuseppe Meazza initially for the season, with a view to a permanent transfer and a four-year contract next summer if the arrangement is successful
The Uruguay international, 28, will spend the 2012-13 campaign at the Giuseppe Meazza on a temporary basis, with the option of a permanent transfer if he impresses.
The club have also confirmed that the tenacious midfielder has agreed terms over a four-year contract if the arrangement is made full-time next summer.
Gargano joined Napoli in the summer of 2007 from Danubio as part of the side's heavy recruitment drive following their return to Serie A, which also included the likes of Ezequiel Lavezzi and Marek Hamsik.
He made 163 Serie A appearances for the Partenopei, scoring four times, but he has opted to move on to pastures new, further aided by the recent arrival of Valon Behrami from Fiorentina.
The South American becomes one of a number of new arrivals at Inter, following in the footsteps of Rodrigo Palacio, Matias Silvestre, Samir Handanovic, Gaby Mudingayi and Antonio Cassano.