The 22 year old 6ft 4in defensive midfielder arrives at Ewood Park on a four year deal after receiving a work permit.
Petrovic started his career at hometown club FK Jedinstvo Ub. A move to Radnicki Obrenovac followed, before he moved to Partizan in the summer of 2008, he has made 19 appearances for Serbia.
Blackburn face a race against time to make sure Petrovic is eligible for Saturday game against Wolves.