The 19-year-old Dutchman signed a new contract last year to keep him at Stamford bridge until 2014 but he will continue his development in the Bundesliga.
The youngster's agent, Wessel Weezenberg, said: "It is important Jeffrey gets playing. For him this is a good step.
"We have chosen stability for Jeffrey. These two years Jeffrey has to play and he can settle in this way. At Chelsea that will be difficult, but in Hamburg the chance is bigger. However, he will have to prove it by himself.
"For him it is a good step. Hamburg is and remains a top team, with a fantastic stadium and a giant fanbase."
Bruma will follow former Chelsea defender Michael Mancienne after the England Under 21 international joined Hamburg last week while Frank Arnesen, who was technical director at Stamford Bridge, is also at the German club.
But Weezenberg added: "Hamburg followed Jeff for years before Arnesen came to work here. The signing of Bruma is based on the impressions of many people at HSV."