The 19-year-old, who played for the USA at the 2014 World Cup in Brazil, will move to HSV for the rest of 2014/15 and will return to the record titleholders at the end of the campaign.
Positive news for Bayern
Green signed professional terms with FC Bayern on 8 November 2013 and has a contract with the Reds until 30 June 2017. While he is yet to make a Bundesliga appearance, that should change in Hamburg, where the objective of his loan is to gain top-flight match practice.
On Sunday, the Bavarians also announced the signing of highly-rated teengaer Sinan Kurt from Borussia Mönchengladbach on a four-year contract. Elsewhere, Javi Martinez is expected back in the Bavarian captial on Monday after undergoing surgery in America, while Arjen Robben has pulled out of the Netherlands squad and will continue his recovery from ankle trouble in Munich.