Rovers, the first Irish side to have progressed to this stage of European football, beat Partizan Belgrade 2-1 on Thursday night to secure a place in Friday's draw.
The clubs are in Group A against Rubin Kazan, from Russia, and Greek side PAOK Salonika.
Fulham face FC Twente from Holland, Odense from Denmark and Wisla Krakow from Poland in Group K.
Stoke will play Dynamo Kiev, Besiktas and Hapoel Tel Aviv in Group E, while Birmingham are in Group H with Club Brugge, Braga and Maribor.
If Celtic are successful in replacing Sion, who are alleged to have breached a transfer ban, they would be in Group I with Atletico Madrid, Udinese and Rennes.
Source: PA
Source: PA