Liverpool will take on LASK, Union Saint-Gilloise and Toulouse in the Europa League group stage while debutants Brighton will face Ajax and Marseille following the draw on Friday.
The Merseyside club, who have lifted the trophy on three occasions, will be hot favourites to qualify top from Group E.
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Brighton face a tough task in their bid to progress past the group stage on their debut in European competition.
Along with former champions Ajax and three-time finalists Marseille, Brighton's third opponents in a strong Group B are Greek champions AEK Athens.
Europa Conference League champions West Ham United were drawn with Olympiacos, Freiburg and TSC Backa Topola in Group A.
Last season's runners-up Roma meet Slavia Prague, Sheriff Tiraspol and Servette in Group G, while 1988 winners Bayer Leverkusen of Germany face Qarabag, Molde FK and BK Hacken in Group H.
The group stage begins from Sept. 21.
The winners of each group advance directly to the round of 16 that will take place from February onwards.
Group runners-up will progress to the knockout stage playoff round, where they will meet one of eight teams that have finished third in their groups in the top-tier Champions League.
Third-placed teams in the Europa League groups will drop to the third-tier Europa Conference League where they will play the group runners-up from that competition in the knockout round playoffs.
The Europa League final will take place at Dublin's Aviva Stadium on May 22 next year.