The 19-year-old has signed a contract that will keep him at the summer of 2014 after passing a medical on Monday.
Tore told Hamburg’s official club website: “I look forward to [playing for] HSV. It is a club with great tradition, which is located in a great city. I will do my best for this club.”
Tore is the third Chelsea player sporting director Frank Arnesen has signed since moving from Stamford Bridge to Hamburg last month.
Hamburg signed Michael Mancienne and Jacopo Sala from the Blues earlier this month.
Arnesen: “Gokhan is a young and extremely talented player, he is left-footed and an offensive [player].
“He is also a physically strong player with good vision. We must, and will, give him the necessary time he needs to continue his positive development in recent years.”
