The 27-year-old East German born midfielder has moved to St Andrews on a loan deal until the end of the season.
However, Forest do have the option to recall Tesche after 28 days should they so wish.
Tesche was signed by former Forest manager Stuart Pearce last summer on a free transfer from Hamburg but has fallen out of favour under new boss Dougie Freedman.
He has made 25 appearances for Forest this season and scored two times.