The Argentina international centre-back completed his switch to the Serie A outfit from Mexican side Monterrey at the beginning of August.
Having opted to switch to Stadio Artemio Franchi, Basanta is now targeting a top-four berth and a possible challenge for the title.
"I had this great opportunity at this particular moment of my career," Basanta said at a news conference.
"It was probably the last opportunity to go to Europe. It was a decision taken with my family.
"Italian football is one of the best in the world and Fiorentina are a great club that wants to grow more and more.
"The objective is to finish in the top four in the standings and who knows, maybe even win a Scudetto."
Basanta made over 200 appearances for Monterrey and played twice at the World Cup as Argentina made the final in Brazil.
