The 23-year-old has spent the past three seasons on temporary deals with Vicenza, Brescia and Valladolid and will now return to Spain's top flight for 2014-15
Rossi will arrive at Estadio Nuevo Arcangel on a temporary basis, although Cordoba have inserted a clause into the deal to enable them to complete a permanent transfer after the 2014-15 campaign.
"Cordoba reserves the right to purchase the player on a permanent deal for the next three seasons," a statement on the Spanish club's website read.
Cordoba finished seventh in the Segunda Division at the end of last season and only qualified for the play-offs due to Barcelona B's ineligibility for promotion.
A 1-1 aggregate draw with Las Palmas in the final saw Cordoba promoted on the away goals rule, and the outfit announced on Friday they had bolstered their midfield options with the signing of former Italy Under-21 international Rossi.
The 23-year-old is yet to make a first-team appearance for his parent club and has spent the previous three campaigns out on loan at Vicenza, Brescia and Real Valladolid.
Rossi featured heavily in La Liga for Valladolid last season, making 31 league appearances - 25 of which were starts - although he was unable to save the club from relegation.