Arsenal will play Udinese in the Champions League playoff round, and four-time winner Bayern Munich was drawn against FC Zurich on Friday.
Lyon received perhaps the toughest draw, against a match-sharp Rubin Kazan which is midway through the Russian league season.
Villarreal will travel to Denmark for the first leg against Champions League newcomer Odense.
Twente will host two-time winner Benfica in the first leg.
In a separate draw for national champions, Copenhagen was drawn against Czech newcomer Viktoria Plzen.
First-leg matches will be played Aug. 16 or 17, and the returns on Aug. 23 or 24.
Ten playoff winners will join 22 teams with direct entry to the group stage, which will be drawn Aug. 25 in Monaco.
Full draw for the playoff round of the Champions League:
First Legs, Aug. 16-17; Second Legs, Aug. 23-24.
Odense (Denmark) vs. Villarreal (Spain)
Twente (Netherlands) vs. Benfica (Portugal)
Arsenal (England) vs. Udinese (Italy)
Bayern Munich (Germany) vs. FC Zurich (Switzerland)
Lyon (France) vs. Rubin Kazan (Russia)
Wisla Krakow (Poland) vs. APOEL (Cyprus)
Maccabi Haifa (Israel) vs. Genk (Belgium)
Dinamo Zagreb (Croatia) vs. Malmo (Sweden)
FC Copenhagen (Denmark) vs. Viktoria Plzen (Czech Republic)
BATE Borisov (Belarus) vs. Sturm Graz (Austria)
