The Korean Football Association (KFA) announced the deal on Friday, almost two months after Hong Myung-bo resigned.
Stielike, who played most of his career at Real Madrid, was last in charge of Al Arabi and has also coached Switzerland and Ivory Coast.
Dutchman Bert van Marwijk was heavily linked with the South Korea position and was reportedly close to signing.
South Korea face Venezuela in a friendly later on Friday and Stielike, appointed until the 2018 World Cup in Russia, is likely to be targeting success at the 2015 Asian Cup.
The appointment of Stielike ends a long wait for the Asian nation.
Hong resigned after the World Cup, where they failed to win a game and finished bottom of Group H.
