Jose Riga has told Blackpool chairman Karl Oyston to deliver on his promises after the two forged an uneasy truce.
Wilfried Bony claims to be fully focused on Swansea at the end of a summer in which his future was called into question.
Brillante underwent a medical on Monday before completing his permanent transfer to the Viola.
"I'm very happy to be in Florence," Brillante said on the club's official website. "I look forward to seeing the team soon.
"I can't wait to get started."
Brillante, who also holds an Italian passport due to his roots, made 46 A-League appearances in his two seasons with the Jets.
The 21-year-old has signed a four-year contract with Fiorentina and becomes the second Newcastle Jets youngster to have moved to a European club since the end of last season.
Australian striker Adam Taggart signed with Fulham last month.
Brillante, who was in Australia's 30-man preliminary squad before being dropped from the final roster for the World Cup in Brazil, will begin pre-season training with his new team in Trentino on Tuesday.
Fiorentina, coached by Vincenzo Montella, finished fourth in Serie A in the 2013-14 campaign and will compete in next season's Europa League.