The Italian defender was set to sign a new four-year contract last week, but the date was pushed back due to the adverse weather conditions.
Astori was then found dead in his hotel room in Udine ahead of the Fiorentina Serie A fixture on Sunday. A judicial investigation into his death was launched on Monday, and an autopsy is set to be carried out.
Fiorentina's club president has since confirmed that the club will honour the contract extension with the wages going to support his immediate family.
The contract is estimated at £1.15million per year, and will go to Astori's long-term partner Francesca Fioretti and their two year old daughter, Vittoria.
There's been an outpouring of grief for the ''Fiore'' captain across Italy which resulted in seven matches in Italy's top flight being postponed following the news of his death.