The 48-year-old made 299 Bundesliga appearances as a player with VfB Stuttgart, FC Nurnberg, Borussia Dortmund, Schalke 04 and 1860 Munich.
His most successful coaching spell came in charge of FC Kaiserslautern, first guiding them to promotion to the top-flight, and then finishing seventh in the 2010-11 Bundesliga season.
Kurz's last coaching role was at Fortuna Dusseldorf in early 2016, where he departed after 7 matches.
Prior to that he also coached at Hoffenheim, 1860 Munich, Ingolstadt and SC Pfullendorf.
Adelaide United chairman Greg Griffin was delighted to have secured the deal.
“We’re delighted, he’s the man we have been pursuing relentlessly,” he was quoted as saying to News Limited.
“He will be given the budget to spend on potential new players including three imports.”
Adelaide United ended a disastrous season earlier this year with a ninth-placed finish in the A-League and a group stage exit in the Asian Champions League. Prior to that, Kurz's predecessor, Guillermo Amor, won the A-League double with the Reds.
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