The 44-year-old took the reins at the Imtech Arena on an interim basis last month following the departure of Mirko Slomka, who paid the price for a poor start to the season following a dismal 2013/14 campaign.
Hamburg were almost relegated from the Bundesliga for the first time in their history last season and Zinnbauer has been charged with the task of turning around their fortunes.
Director of football Peter Knabel stated earlier this month that he was keen for Zinnbauer to be awarded a longer contract and Hamburg revealed on Monday that he has put pen to paper on a permanent deal.
Zinnbauer's side sit third-bottom of the table after losing 3-0 at Hertha Berlin on Saturday, but prior to that he masterminded a 1-0 victory at Borussia Dortmund and a 1-1 draw with second-placed Hoffenheim.
Hamburg host Bayern Munich in the DFB Pokal on Wednesday, then entertain Bayer Leverkusen in the Bundesliga three days later.
