The Italy international and Fiorentina defender was found dead in his hotel room in the north-eastern city of Udine on March 4 ahead of a Serie A match against Udinese.
He left behind his parents, girlfriend Francesca and their two-year-old daughter Vittoria.
"The idea of the trust is to contribute to the economic security of little Vittoria and will be managed by the Astori family and her mother Francesca," the club said.
"With this gesture we hope that we will display in the name of the team and the fans the love and respect we all hold towards Davide."
On Sunday, Fiorentina play their final home game of the season against Cagliari, a team where Astori began his professional career and played for six seasons.
Players from the Sardinian team on Saturday paid tribute to Astori by placing flowers outside the Artemio Franchi Stadium where hundreds of scarves, banners and drawings pay tribute to the former international.
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