"This is a huge tragedy for us. I don't even know how to express this pain. We are all under shock.
"He was with us for four years and just think that he was due to extend his contract on Monday.
"He was due to do it earlier, but due to the snow, we had put it back and agreed we would do it on Monday.
"It was his greatest joy to be able to end his career here, because this is where it would have ended."
Astori was found dead in his hotel room on Sunday at the age of 31 after a suspected cardiac arrest before an Italian league match.
The defender, who has also played 14 times for Italy's national team, was discovered by Fiorentina teammates when he failed to show up for breakfast at the hotel in Udine.
Fiorentina's game at Udinese in northeast Italy was called off, along with all fixtures in the country's top two divisions.
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Fiorentina said Astori, who had played for the club since 2015, was "hit by a sudden illness".
"For this terrible and delicate situation, and above all out of respect for his family, we appeal to the sensitivity of everyone," the team said in a statement.
Astori leaves behind a wife and 2-year-old daughter.