The 22-year-old striker is set to join Los Che on a five-year deal for an undisclosed fee from the recently relegated Andalusians, with a friendly between the two clubs also being part of the agreement.
A quarter of the transfer fee will be paid to Estudiantes, Piatti's first club, as part of a sell-on clause dating back to the player's move to Spain in 2008.
Valencia president Manuel Llorente said: "He is a young player who has made a speedy progression but also has much experience at the highest level.
"We are happy to have him as part of the squad. I can reveal now that there was a long and secretive negotiation process, but we have got the result that we wanted.
"Piatti is also from the province of Cordoba that has given us players such as (Mario) Kempes, Claudio Lopez and (Pablo) Aimar, so let's hope this is a good sign."