The 26-year-old joins the Rams as their third summer signing after becoming a free agent following the expiration of his deal with SC Paderborn.
Bilbija spent the last three seasons with the German second-tier club, making 89 Bundesliga 2 appearances and scoring 29 goals.
Comfortable as an attacking midfielder, winger or central striker, he enjoyed the best season of his career last term, netting 17 goals in all competitions.
His highlights included four goals in a thrilling 4-3 win over Magdeburg and a crucial header in Paderborn’s 2-1 promotion play-off victory against Wolfsburg.
The move marks Bilbija’s first experience outside Germany after spells with Ingolstadt, Hamburger SV and Paderborn. He has joined John Eustace’s squad in Austria.