Astori passed away from cardiac arrest in March, the night before Fiorentina's league fixture against Udinese.
Football fans all over the world were quick to offer their condolences to the family, who released an appreciative statement on Saturday.
"Thank you from the heart. It's a simple but unique term, just like Davide was," they told La Nazione.
"Therefore, as Davide would have done, with a smile and a strong embrace, we say to you all thank you."
Fiorentina are also set to rename their training ground in memory of the Italian defender.