The Scottish Premiership outfit saw off the challenge of Swedish club Elfsborg in the previous round, but now they face the long trip to Eastern Europe as they attempt to progress through to the main draw.
After being seeded for the draw, Celtic will play the first leg away from home, which will take place on the week commencing August 19.
The return leg will then take place at Celtic Park a week later, with the winners progressing through to the illustrious group-stage draw that will take place at the end of August.
Full 'Champions' route draw:
FC Steaua Bucuresti vs. Legia Warszawa
FC Shakhter Karagandy vs. Celtic
FC Viktoria Plzen vs. NK Maribor
PFC Ludogorets Razgrad vs. FC Basel
GNK Dinamo Zagreb vs. FK Austria Wien