The Gunners were handed the tricky fixture despite being seeded in the 'League route' of the draw for teams that did not win their domestic title.
Besiktas showed their potential in the previous round by beating Feyenoord home and away with a hat-trick from new signing Demba Ba wrapping up a 5-2 aggregate victory with a 3-1 win in Istanbul..
However, the Gunners will be encouraged by how easily they disposed of fellow Turkish outfit Fenerbahce (5-0 on aggregate) at the same stage last season.
"It's nice we have got the second leg at home," Arsenal club secretary David Miles said.
"They (the playoff ties) come relatively early in the season, and our three German World Cup winners won't even be back, or will be just starting training then, so probably we won't have the full squad to choose from,
"Nevertheless, we've got a good squad, quality in depth and I'm sure will be okay."
Celtic were draw against Slovenian outfit Maribor in the 'Champions route' less than two hours after learning they were back in Europe's top competition following Legia Warsaw's elimination for fielding an ineligible player.
Both Arsenal and Celtic will be at home for the second legs of their clashes.
Napoli, bidding to reach the Champions League group stage for the third time and the second in a row, were handed a daunting tie against Athletic Bilbao.
Rafael Benitez's Napoli finished third in Serie A last season, only enough for a place in the playoff round after Italy slipped down the national coefficients which determine how many places each league gets in the tournament.
Bilbao, fourth in La Liga, were beaten Europa League finalists in 2012.
Twice former champions Porto were also handed a difficult draw as they were paired against Lille, with the French club at home the first leg.
Former European champions Steaua Bucharest were paired with Bulgaria's Ludogorets Razgrad while Cypriot champions APOEL Nicosia, who reached the quarter-finals two seasons ago, were drawn against Danish counterparts AaB Aalborg.
Malmo, runners-up in 1979, play Austrian champions Salzburg, who are attempting to reach the group stage for the first time since Red Bull's takeover in 2005.
FC Copenhagen will meet Bundesliga side Bayer Leverkusen, Belgium's Standard Liege face Zenit St Petersburg and Slovan Bratislava play Belarusian champions BATE Borisov in the other of the 10 ties.
UEFA said that the vanishing spray, used at the World Cup to display the correct distance between a free kick and the defensive wall, would be used in the tournament, starting with the playoff round.
Maribor (Slovenia) v Celtic (Scotland)
Salzburg (Austria) v Malmo (Sweden)
AaB (Denmark) v APOEL (Cyprus)
Steaua (Romania) v Ludogorets (Bulgaria)
Slovan Bratislava (Slovakia) v BATE (Belarus)
Besiktas (Turkey) v Arsenal (England)
Standard Liege (Belgium) v Zenit (Russia)
Copenhagen (Denmark) V Bayer Leverkusen (Germany)
Napoli (Italy) v Athletic Bilbao (Spain)
Matches to take place August 19/20 and August 26/27
- Sports & Recreation