Hamburg, Germany – Another Chelsea player swapped London for year contract.
Rajkovic moved to Stamford Bridge in 2007 but was unable to lock down a place in the first team as he failed to make a start for the Blues.
The 22-year-old spent time on loan with PSV Eindhoven, Twente and Vitesse before Chelsea allowed him to make a permanent switch on Wednesday.
Former Chelsea director Frank Arnesen is now at Hamburg, and he has used his connection with the English club to lure Michael Mancienne, Gokhan Tore, Jacopo Sala and Jeffrey Bruma to Germany this summer from England.
Hamburg has started the new Bundesliga campaign in poor form with just one point from its first three games.