The 43-year-old takes the reins from interim coach Frank Kramer, who assumed first-team duties following the dismissal of Markus Babbel on 3 December.
As a player, Kurz made 300 Bundesliga appearances for VfB Stuttgart, 1. FC Nuremberg, Borussia Dortmund, Borussia Mönchengladbach, FC Schalke 04 and 1860 Munich, winning the title in 1995 with Dortmund and the UEFA Cup two years later with Schalke.
The former defender began his coaching career with SC Pfullendorf before a spell at 1860. He then led 1. FC Kaiserslautern back into the Bundesliga in 2010, a year after taking the helm.