Juventus announced on Wednesday they had signed Torino defender Bremer a little over 24 hours after Matthis de Ligt left for Bayern Munich.
The 36-time Italian champions have paid 41 million euros ($41.7 million) for 25-year-old Brazilian Bremer, who had joined their local rivals in 2018 from Atletico Mineiro.
Netherlands centre-back de Ligt left Juve on Tuesday after three seasons.
"The Bianconeri defence has been strengthened by the arrival of Gleison Bremer, who today signed a contract that ties him to Juventus on a permanent deal until 2027," Juve said.
"In his time in Italy he has emerged as one of the best defenders in circulation, confirmed by the MVP award from Lega Serie A as Best Defender for season 2021-22," they added.
Massimiliano Allegri's side have also signed the likes of France World Cup winner Paul Pogba and Argentina attacker Angel Di Maria as they eye a first league title since 2020.
After a record nine consecutive Scudetti (2012 to 2020), the 'Old Lady' have been outside the top three in Serie A for the past two seasons and have not reached the quarter-finals of the Champions League since 2019.
Earlier on Wednesday, Paulo Dybala joined Roma after his deal with Juve expired.