Tesche is Gary Rowett's first capture of the summer 2016 transfer window and his contract will run from 1 July 2016 until 30 June 2019.
The 29-year-old free agent, previously had a successful loan spell at St. Andrew's at the end of the 2014/15 season, where he scored twice in 12 appearances.
A skilful, ball-playing midfielder, he is able to dictate the play and is adept at shooting from distance.
Blues had previously attempted to bring Tesche back at the start of last season, but were unable to do so after a change in management at his previous club, Nottingham Forest.
Despite missing several months at the start of last season with a broken foot, Tesche went on to make 25 appearances and score one goal for the Reds.
Born in the former East German city of Wismar, Tesche began his footballing career with Arminia Bielefeld before making the switch to Hamburg, where he remained for five years.
In August 2014, he was picked up by former Forest boss Stuart Pearce on a free transfer and went on to make a total of 50 appearances for the Reds and find the back of the net three times.