In an update on the 22-year-old's condition said: "ACF Fiorentina has announced that Edoardo Bove, following an uneventful night, was awakened and extubated this morning. He is currently awake, alert and oriented.
"He has spoken with his family, club management, the coach and his team-mates, who all rushed to go and see him as soon as they heard the good news. Further tests will be carried out in the coming days to establish what led to the critical situation that took place yesterday.
"The doctors at Careggi University Hospital who are treating the player have confirmed that diagnostic tests are ongoing. Fiorentina would like to thank Careggi University Hospital and all of the doctors and staff for the wonderful humanity and professionalism they have shown.
"The club would also like to thank the wider Fiorentina family and the entire world of football who, during this difficult time, have shown their great sympathy and care through their messages and support, which have been of great comfort both to the club and Edoardo and his family."
Sunday's game was abandoned after the 22-year-old fell to the ground in the 17th minute. Fiorentina and Inter players formed a shield around him before he was taken away. The referee took his time to talk with both sides and then the game was abandoned.
An earlier Fiorentina statement said "initial cardiological and neurological tests have ruled out acute damage to the central nervous system and the cardio-respiratory system."
Bove has made several appearances for Italy's Under-21 team and has recorded four assists and one goal in his 14 appearances for Fiorentina this season
with agencies