The two clubs agreed a deal for the 19-year-old Dutchman earlier this month and the move was formally rubber-stamped on Thursday as Bruma put pen to paper on a 12-month deal with an option for a further year.
"Hamburg is the best option for me," Bruma told Hamburg's official website www.hsv.de.
"Here, I can play at the highest level in Germany."
Hamburg sporting director Frank Arnesen played a key role in luring Bruma to HSV, just a few weeks after taking up his new role after leaving a similar post at Stamford Bridge.
Bruma, who is under contract at Chelsea until 2014, will join up with former Blues team-mates Michael Mancienne, Jacopo Sala and Gokhan Tore, all of whom recently penned permanent deals at the Imtech Arena.
He added: "HSV has long been interested in me."
The Holland international made his first-team Chelsea debut in late 2009 and has since made nine appearances for the club.
He also spent three months on loan at Leicester last season, making 11 appearances for Sven-Goran Eriksson's side.
Source: PA
Source: PA