The 36 year-old flew into Florence and is expected to undergo a medical before putting pen to paper on what will reportedly be a two-year contract.
Fiorentina shared to social media a photo of Ribery on the tarmac wearing a club scarf and polo with the caption: "#WelcomeLegend".
Addressing reporters outside the airport, the former Bayern Munich star was quoted as saying: "I am here with my family. We're doing something together.
"I have already spoken to Fiorentina and Luca Toni, who told me this was a great club and a beautiful city."
Ribery became a free agent when his Bayern contract expired at the end of June.
He spent 12 years in Bavaria, winning 23 trophies including nine Bundesliga titles and the Champions League.
The ex-Marseille star had been linked to Sheffield United, A-League side Western Sydney Wanderers and teams in Saudi Arabia and Qatar.