Astori, 31, was found dead in his hotel room in Udine on Sunday evening (AEDT), hours before Fiorentina were due to face Udinese. No cause of death has yet been identified.
Udinese v Fiorentina and the rest of the day's scheduled Serie A matches were postponed as tributes flowed for the popular Italy international.
Fiorentina president Andrea Della Valle told reporters Astori had been due to sign a new contract on Monday and Lega Calcio special commissioner Giovanni Malago has confirmed the club will honour this agreement to support Astori's long-term partner Francesca Fioretti and their two-year-old daughter Vittoria.
"It is something we all appreciate a lot and a sign of huge sensitivity by the Della Valle family," Malago said. "They decided to renew Astori's contract and the money will support Davide's family. It's very honourable of them to take such a decision.
"Thanks to Diego [Della Valle] and Andrea and thanks to [Fiorentina executive chairman] Mario Cognigni. They really did a nice action."
Astori's funeral will be held on Friday (AEDT) at Florence's Basilica di Santa Croce.