The match, plus all Serie A fixtures on Sunday, were subsequently called off.
In 2014, Astori agreed a season-long loan to Roma for £1.8m and the Giallorossi paid a further £4.5m to make the deal permanent.
Former Roma manager Rudi Garcia tweeted: "The news of the untimely death of my former player Davide Astori pains me".
Astori who had 14 global caps to his name, was found dead at the Ladi Moret hotel in Udine, ahead of the Viola's meeting with Udinese on Sunday.
Conte said: "This is a tragedy and it really hurts me".
"Fiorentina are profoundly shocked to have to announce the death of captain Davide Astori after a sudden illness", Fiorentina said.
The defender, who was also capped 14 times by the Italian national team, scoring one goal in the blue of the Azzurri, was due to sign a contract Monday that would have seen him spend the rest of his career at the club. He was a great player but especially a fantastic guy.
Tributes from former teams, coaches, and teammates spread across social media on Sunday.
DAVIDE ASTORI was born in Bergamo and played for local team Pontisola before joining AC Milan in 2006. I stay close to his wife, parents and daughter.
Astori's body was taken to the Santa Maria della Misericordia Hospital for an autopsy. His debut in March 2011 in a 2-0 victory over Ukraine in Kiev was eventful - he was introduced as a first-half substitute before being sent off with 15 minutes remaining after receiving two yellow cards. Italy would go on to win the match on penalty kicks.
Astori scored his only global goal in the 2013 FIFA Confederations Cup third-place play-off against Uruguay in Salvador, giving Italy a first-half lead in a match which finished 2-2. I don't believe it and I cry with the family and everyone at Fiorentina.
Cesare Prandelli, Astori's coach in most of his Italy games, said he was "deeply upset, I feel a great emptiness inside".