Arsene Wenger's side are preparing for their 17th successive season in Europe's elite club competition and will face the Superliga side for the first time in their history when they attempt to secure a place in the group stage.
The two-legged tie will see former Chelsea striker Demba Ba return to London against a club he was linked with before agreeing a four-year deal on July 18.
Ba has already made an immediate impact in Turkey with a hat-trick on his debut against Feyenoord in the third qualifying round.
Ligue 1 side Lille stand in the way of Porto, winners of the competition in 2004, and a fourth successive group stage appearance, while Bayer Leverkusen will meet Copenhagen.
Standard Liege must beat Russian Premier League runners-up Zenit if they are to reach the group stage for the first time since 2009-10, and Rafael Benitez faces a trip back to Spain when his Napoli side face Athletic Bilbao.
Free-scoring Red Bull Salzburg will attempt to continue their progress in the competition against Malmo, the Austrian champions have already scored 16 goals in five competitive matches this season and came past Qarabag 3-2 in the third qualifying round.
Having been handed a reprieve by UEFA after Legia Warsaw fielded an ineligible player, Bartosz Bereszynski, in the second leg of the third qualifying round Celtic will meet Maribor, while Aalborg face APOEL and Slovan Bratislava take on BATE Borisov.
Steaua Bucharest, 1986 winners of the competition in its former guise as the European Cup, were drawn against Latvian champions Ludogorets.
The first legs will be played on the August 19 and 20, with the return matches a week later.
Champions League play-off draw in full:
Maribor v Celtic
Red Bull Salzburg v Malmo
Aalborg v APOEL
Steaua Bucharest v Ludogorets
Slovan Bratislava v BATE Borisov
Besiktas v Arsenal
Standard Liege v Zenit
Copenhagen v Bayer Leverkusen
Lille v Porto
Napoli v Athletic Bilbao
