Their fourth-placed finish in the Premier League last season means the Gunners once again take part in the preliminary stage, although they should be relatively confident of making it through.
Last season saw them claim a convincing 5-0 aggregate win over Fenerbahce at the same stage and boss Arsene Wenger will be hoping for a similarly easy time to see the Gunners through to the group stages for the 15th consecutive year.
Here is the full draw for the play-off stage, per Purely Football:
First leg to take place on Aug. 19, second leg on Aug. 27.
Wenger will have to utilise his squad well during August as the games come thick and fast for Arsenal early on, with the Community Shield against Manchester City, three Premier League matches and the two-legged Champions League play-off.
One of Arsenal's key issues last season, which saw them slip out of contention for the Premier League title, was injury issues and lack of depth.
Although most of his players will hopefully be fresh and raring to go so early in the season, his World Cup-winning trio Mesut Ozil, Per Mertesacker and Lukas Podolski are set to miss the Premier League opener against Crystal Palace.
Between the two legs of the play-off tie is a very tricky encounter away at Everton in the Premier League, which Arsenal will be desperate not to lose to avoid losing pace early in the season.
However, with key additions made to the squad over the summer, Arsenal should have enough quality to get off to a strong start in all competitions in the 2014-15 season.
Besiktas finished in third place in the Turkish league last year and will provide stiff opposition for the Gunners, especially with the first leg away in Istanbul, a 3,000-mile round trip.
As the Telegraph's Jeremy Wilson points out, the travelling distance will be a major concern for Wenger.
Besiktas beat Eredivisie runners-up Feyenoord 5-2 on aggregate in the previous qualifying round, new man Demba Ba scoring a hat-trick in a 3-1 second-leg victory.
The former Chelsea and Newcastle man will likely be the biggest goal threat for the Turkish side against Arsenal and his experience of facing the Gunners should be helpful.
However, Arsenal simply need to not lose the first leg as they should be able to overcome Besiktas at home.
As with last year, a trip to Istanbul is not ideal. But they saw off Fenerbahce with ease and should do so again with Besiktas to see themselves through to the group stages.
Prediction: Arsenal to win 3-1 on aggregate