Monaco - Marseille, last season's beaten Europa League finalists, were drawn with Lazio and Eintracht Frankfurt in a strong Europa League group on Friday.
Arsenal were handed a seemingly easier task against Sporting Lisbon, Azerbaijani club Qarabag and Vorskla of Ukraine.
The other English club in Europe's second-tier competition, Chelsea, will play PAOK Salonika, BATE Borisov from Belarus and Hungarians Vidi.
Scottish champions Celtic are in a group that includes the two Red Bull-owned clubs - Salzburg, a beaten semi-finalist last season, and Leipzig - as well as Rosenborg of Norway.
Rangers, a fourth seed, face a tough task progressing on their return to Europe against Villarreal, Rapid Vienna and Spartak Moscow.
Dudelange, the first club from Luxembourg to reach the group stage of the competition, were handed a trip to the San Siro to play AC Milan, who have won eight European trophies, and will also face Real Betis and Olympiakos.
Antoine Griezmann, who scored twice in last season's final as Atletico Madrid beat Marseille 3-0, was named the Europa League player of last season.
Griezmann, a World Cup winner with France, also finished fourth in the UEFA player of the season award announced on Thursday and won by Croatian Luka Modric, a winner in the Champions League final and runner-up in the World Cup.
The first round of matches will be played on Thursday, September 20
Group A: Bayer Leverkusen (GER), Ludogorets (BUL), Zürich (SUI), AEK Larnaca (CYP)
Group B: Salzburg (AUT), Celtic (SCO), RB Leipzig (GER), Rosenborg (NOR)
Group C: Zenit (RUS), København (DEN), Bordeaux (FRA), Slavia Praha (CZE)
Group D: Anderlecht (BEL), Fenerbahçe (TUR), Dinamo Zagreb (CRO), Spartak Trnava (SVK)
Group E: Arsenal (ENG), Sporting CP (POR), Qarabag (AZE), Vorskla Poltava (UKR)
Group F: Olympiacos (GRE), AC Milan (ITA), Real Betis (ESP), Dudelange (LUX)
Group G: Villarreal (ESP), Rapid Wien (AUT), Spartak Moskva (RUS), Rangers (SCO)
Group H: Lazio (ITA), Marseille (FRA), Eintracht Frankfurt (GER), Apollon (CYP)
Group I: Besiktas (TUR), Genk (BEL), Malmö (SWE), Sarpsborg (NOR)
Group J: Sevilla (ESP), Krasnodar (RUS), Standard Liège (BEL), Akhisar Belediyespor (TUR)
Group K: Dynamo Kyiv (UKR), Astana (KAZ), Rennes (FRA), Jablonec (CZE)
Group L: Chelsea (ENG), PAOK (GRE), BATE Borisov (BLR), Vidi (HUN)