Blackburn chief executive John Williams said: "Vratislav has been at Ewood Park today and we have completed the paperwork.
"He is now looking forward to meeting up and training with the rest of the squad. He is excited by the move and very keen to get involved."
Rovers boss Graeme Souness is now hopeful of receiving international clearance in order for Gresko to be included in the squad to face Aston Villa on Sunday