Celtic, who edged Dinamo Moscow in the previous round, will host the first leg against the Premier League outfit who are entering the fray at the final qualifying stage.
Atletico Madrid must face Panathinaikos while Fiorentina were drawn against Sporting Lisbon in other ties.
Rank outsiders Sheriff Tiraspol of Moldova, who stunned Slavia Prague in the previous round, were drawn against group stage regulars Olympiakos.
The group stage will also feature a club from either Austria or Israel after Salzburg and Maccabi Haifa were drawn together.
Champions League Play-off draw
Oympique Lyon (France) v Anderlecht (Belgium)
Celtic (Scotland) v Arsenal (England)
FC Timisoara (Romania) v VfB Stuttgart (Germany)
Sporting (Portugal) v Fiorentina (Italy)
Panathinaikos (Greece) v Atletico Madrid (Spain)
Sheriff Tiraspol (Moldova) v Olympiakos Piraeus (Greece)
Salzburg (Austria) v Maccabi Haifa (Israel)
FK Ventspils (Latvia) v FC Zurich (Switzerland)
FC Copenhagen (Denmark) v APOEL Nicosia (Cyprus)
Levski Sofia (Bulgaria) v Debrecen (Hungary)
* First legs to be played on August 18 and 19.
* Second legs to be played on August 25 and 26.