The Gunners have been tasked with getting past a Turkish club for the second year in a row following their 5-0 aggregate victory over Fenerbahce last season
The Turkish outfit finished third in their domestic league last season and entered the competition at the third qualifying round.
Demba Ba, who left Chelsea for Besiktas this summer, scored a hat-trick in the second leg as his side eliminated Feyenoord 5-2 on aggregate.
Other notable match-ups in the draw see Serie A outfit Napoli take on Athletic Bilbao in what is arguably the tie of the round, while Celtic will take on Maribor - pending Leagia Warsaw's appeal against their withdrawal from the tournament.
Arsenal fans and players alike have already reacted to the draw, with Mesut Ozil taking to Twitter to voice his excitement.
Arsenal won 3-0 away at the Sukru Saracoglu Stadium, before a double from Aaron Ramsey at the Emirates saw the north London side comfortably through to the group stages.
The Gunners have never played Besiktas before but have a strong record against Turkish sides in European competition - having played seven matches and never lost in normal or added time.
The only blip on that record was the Uefa Cup final in 2000. The build up to the match in Copenhagen was marred by fan violence as Arsene Wenger's side lost on penalties to Galatasaray.
CHAMPIONS LEAGUE PLAY-OFF DRAW IN FULL
Maribor (SVN) v Celtic (SCO)
Salzburg (AUS) v Malmo (SWE)
AaB (DEN) v Apoel (CYP)
Steaua Bucharest (ROM) v Ludogorets (BUL)
Slovan Bratislava (SVK) v BATE Borisov (BLR)
Besiktas (TUR) v Arsenal (ENG)
Standard Liege (BEL) v Zenit St Petersburg (RUS)
FC Copenhagen (DEN) v Bayer Leverkusen (GER)
Lille (FRA) v Porto (POR)
Napoli (ITA) v Athletic Bilbao (SPA)