The 23-year-old has agreed to move to the San Siro when his contract expires at the end of the season.
Botta came through the Boca Juniors youth academy but never made an appearance for the Buenos Aires-based club, signing for Tigre as a 19-year-old in 2009.
It is believed the playmaker has put pen-to-paper on a five-year deal with Andrea Stramaccioni's men.
"I am very happy to have the chance to play in one of the most important teams in the world," he told Corriere dello Sport.
"It is an honour for me to have the chance to wear the Inter shirt and play alongside players like Javier Zanetti, Esteban Cambiasso, Diego Milito and others."