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 other ties include Olympique Lyon v Anderlecht and Sporting Lisbon v Fiorentina.
Rank outsiders Sheriff Tiraspol, who stunned Slavia Prague in the previous round, were drawn against group stage regulars Olympiakos in the meeting of the Moldovan and Greek champions.
The group stage will also feature a club from either Austria or Israel after Salzburg and Maccabi Haifa, the champions of the respective countries, were drawn together.
Latvia or Switzerland will also be represented after FK Ventspils were paired with FC Zurich and one of Bulgaria or Hungary will feature after Levski Sofia were drawn with Debreceni.
UEFA have introduced a new system this season in which teams who are champions of their respective nations are kept apart from non-champion teams.
The system is designed to give the smaller nations a better chance of being represented in the group stage as they do not have to face non-champion teams from countries such as England, Germany, Spain and Italy in the qualifying rounds.
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"These new arrangements will mean that we will have at least another five national association champions joining those 13 that have already directly qualified for the group stage," said UEFA general secretary David Taylor.
"The format may be not such a big change compared to past qualifying formats, but it does highlight the 'champions' aspect of the UEFA Champions League.
Sheriff Tiraspol, who beat Finland's International Turku in the second qualifying round, had been hoping for an easier draw.
"We were expecting something a little bit easier such as maybe the Bulgarian outfit," said Sheriff's representative Maxim Wilhelm. "But it's a good chance to show what we can do in the final round."
Champions League play-off draw:
FC Sheriff vs Olympiakos
SV Red Bull Salzburg vs Maccabi Haifa
FK Ventspils vs FC Zurich
FC Copenhagen vs Apoel Nicosia
Levski Sofia vs Debrecen
Lyon vs Anderlecht
Celtic vs Arsenal
FC Timisoara vs VfB Stuttgart
Sporting vs Fiorentina
Panathinaikos vs Atletico Madrid
First legs are to played August 18/19. Second legs August 25/26.
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