The USA international, who scored against Belgium at the World Cup, will continue his career at Hamburg after sealing a loan deal for the 2014-15 season
HSV were keen to add some fresh blood to their squad before the end of the transfer window following their disappointing start to the 2014-15 season and they have now brought in the 19-year-old Green on deadline day.
Green came through the ranks of the Bayern and made his official first-team debut in last season's Champions League win over CSKA Moscow in November 2013.
The USA international, who scored once at the 2014 World Cup, was unlikely to get much playing time this season due to the stiff competition for places, however, and has therefore been shipped out on loan in order to gain valuable first team experience.
The versatile attacker has a contract with Bayern Munich that will keep him at the club until June 2017.