The left-back, who celebrates his 22nd birthday on Friday, joins the Bundesliga club on a four-year deal following two and a half seasons in the Japanese top flight with his first professional club.
Kim was named in South Korea's initial 23-man squad for the FIFA World Cup, but was forced to withdraw after failing to overcome an ankle ligament injury.
His place was taken by another Germany-based Korean in the shape of Mainz full-back Park Joo-ho.
However, Kim has used his unwanted break as a chance to resolve his long-term future.
Kim started all 76 of his career appearances for Albirex Niigata, meaning he is yet to come off the bench as a professional - a record that also stretches to his nine international caps.
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