The 43-year-old, who left Kaiserslautern in March following a 16-game run without a win, will officially take over from January 1, Hoffenheim said in a statement.
Kurz replaces interim boss Frank Kramer, who had stepped in after the sacking of Marcus Babbel earlier this month and will now return to the Hoffenheim U23 team.
Hoffenheim have completed their worst first half to a Bundesliga season and go into the mid-season break in the relegation play-off spot after a run of six straight defeats and only one win in their last 12 matches.
Kurz, who played 300 Bundesliga matches and won a German league title with Borussia Dortmund as well as the 1997 UEFA Cup with Schalke, has also coached second tier 1860 Munich.
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