The 52-year-old German, who had previously managed Samsunspor and Ludogorets, is to manage the team for two seasons.
Reis is set to receive €1 million for the 2026/27 season and €1.2 million for the 2027/28 season.
Trabzonspor lost 1-0 to Konyaspor last Saturday and will face Galatasaray this Saturday.
The Black Sea club strengthened their squad last month with the signings of former Liverpool players Mohamed Salah and Fabinho.