The Serie A side revealed last week that they had agreed a deal with the Mexican club for the versatile 30-year-old.
And Fiorentina confirmed on Friday that Basanta has passed a medical and sealed his move to Florence.
The Italian club said in a statement: "Fiorentina communicate that it has purchased outright the rights to player Jose Maria Basanta from Monterrey.
"Basanta was born in Buenos Aires (Argentina) on April 3, 1984. In the last six seasons he has been at Monterrey, where he also wore the captain's armband, and where he won two Mexican championships and three CONCACAF Champions Leagues.
"The defender has also played 12 times for the Argentine national team, participating in the last World Cup."
Basanta made over 200 appearances for Monterrey and featured twice for his country - against Belgium and Switzerland - at the recent World Cup in Brazil.