The 29-year-old Brazilian international leaves VfL Wolfsburg after four years, 142 appearances and 12 goals.
A former Corinthians Alagoano, 1899 Hoffenheim and Bayern Munich defensive midfielder, Gustavo has 41 national team caps.
Speaking to the club’s official website upon his departure from VfL, Gustavo thanked Wolfsburg for all they have done for him over the years.
He said: “I would like to thank my teammates, the coaching staff, the management, the staff and above all the VfL fans for a great period that I’ll never forget.
“My family and I have been greatly accepted here and have felt at home in Wolfsburg since day one. Although it’s not easy for me to say goodbye, I’ve felt a growing desire over the summer to try something new and experience a different country and a different league.”
Wolfsburg sporting director Olaf Rebbe added: “Luiz Gustavo has been an important player for Wolfsburg in recent years and we would’ve liked to have kept him. However we decided to comply with his desire to move as he’s always given everything for VfL during his four years here.
“Not only did he play a big part in our successes in the Bundesliga and DFB Cup, but he was also a leading player for us during the difficult season just gone and his performances helped us to avoid relegation. We’re pleased for him that he can gain more new experiences and prove himself at the top level again in Ligue 1 and the Europa League.”