The U.S. national team midfielder will continue his career at Hamburg after sealing a loan deal for the 2014-15 season.
Green came through the ranks of the Bayern youth system and made his official first-team debut in a Champions League win over CSKA Moscow in November 2013.
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The German-American, who committed to the U.S. program in March and scored in the Americans' round of 16 loss to Belgium at the World Cup, was unlikely to get much playing time this season because of the stiff competition for places.
The winger has a contract with Bayern Munich that will keep him at the club until June 2017.
HSV was keen to add some fresh blood to its squad before the end of the transfer window following their disappointing start to the 2014-15 season.