Basanta has made over 200 appearances for the Mexican side, but his six-year stay at the club is now at an end with a move to Europe in the offing.
The 30-year-old will complete his move to Stadio Artemio Franchi upon the successful completion of a medical and the agreement of personal terms.
A statement on Fiorentina's official website read: "Fiorentina announces that it has reached an agreement with Monterrey for the outright purchase of footballer Jose Maria Basanta.
"[The deal] is subject to the successful medical examinations and contract being signed by the player."
Basanta was part of the Argentina squad that reached the final of the World Cup, where they lost 1-0 to Germany earlier this month.
He made two appearances in the tournament, against Switzerland in the round of 16 and Belgium in the next round.