The defender died following a "sudden illness" the night prior to a Sunday match with Udinese, his club confirmed on their official Twitter feed.
The game was postponed along with all of Sunday's other Serie A fixtures. He was a great player and I had the pleasure of having him in the national team. "It's sad what has happened, but once you are on the pitch, it's hard to think about other things".
"Our sincerest condolences to the family and friends of Fiorentina captain and Italian worldwide Davide Astori, who passed away suddenly last night", European football's governing body UEFA said on social media.
Stadio Artemio Franchi, Florence, Italy - February 9, 2018 Fiorentina's Davide Astori reacts.
Fiorentina president Andrea Della Valle said Astori had been due to sign a new contract on Monday that would have kept him at the Florence-based club for the rest of his playing career. With the screening that we do and the pre-performance checks for professional athletes, the risks of sudden death can be ruled out by up to 89 percent.
"The belief is that the player died of a cardiac arrest by natural causes", Udine prosecutor Antonio De Nicolo said. It's very hard at this moment to find the right words for the family.
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"We opened an investigation for manslaughter", De Nicolo said.
Conte said: "This is a tragedy and it really hurts me".
Clubs across Europe will now also pay their respects, including Serie A sides Juventus, AC Milan and Lazio.
Radja Nainggolan, Astori's former Cagliari teammate wrote on Instagram: "A great player, but even more than that, a great person".
The newspapers, including La Gazzetta dello Sport, Corriere dello Sport and Tuttosport, mentioned the death of 31-year-old Astori on their front pages. I feel like crying knowing that he has left a wife and a two-year-old daughter, who will grow up not knowing her dad.
European games in the Champions League and Europa League will all be preceded by a minute's silence in midweek.