The Gunners have qualified for the Champions League group stages for the past 15 years, but they will face a formidable task if they are to continue that run for a 16th campaign.
Fenerbahce finished second in their domestic league last season, while they also made it through to the last four of the Europa League.
Several members of their squad will be familiar to Arsenal supporters, with former Liverpool duo Dirk Kuyt and Raul Meireles currently with the Turkish giants, while Joseph Yobo also plies his trade with Fenerbahce.
Full 'League' route draw:
Fenerbahce vs. Arsenal
PSV Eindhoven vs. AC Milan
FC Pacos de Ferreira vs. Zenit St Petersburg
Schalke 04 vs. Metalist Kharkiv
Lyon vs. Real Sociedad