It is the first time in 20 years that the Gunners, who finished fifth in the Premier League last season, have started a season in Europe's second-tier competition.
Everton are in the same group as Lyon, who host the final on 16 May 2018.
The Toffees will also face Italian Serie A side Atalanta and Apollon Limassol of Cyprus.
Everton, who completed their play-off victory over Croatian side Hajduk Split on Thursday, are in Europe for the first time since 2014-15.
The 48-team draw for this season's competition included Sweden's Ostersund, managed by Englishman Graham Potter, the former Stoke City and West Brom full-back.
Ostersund will play Spain's Athletic Bilbao, Germany's Hertha Berlin and Zorya Luhansk of Ukraine.
The group stage begins on 14 September.
Group A: Villarreal, Maccabi Tel Aviv, Astana, Slavia Prague.
Group B: Dynamo Kiev, Young Boys, Partizan Belgrade, Skenderbeu.
Group C: Sporting Braga, Ludogorets, Hoffenheim, Istanbul Basaksehir.
Group D: AC Milan, Austria Vienna , Rijeka, AEK Athens.
Group E: Lyon, Everton, Atalanta, Apollon Limassol.
Group F: FC Copenhagen, Lokomotiv Moscow, Sheriff Tiraspol, FC Zlin.
Group G: Vitoria Plzen, Steaua Bucarest, Hapoel Beer-Sheva, FC Lugano.
Group H: Arsenal, BATE Borisov, Cologne, Red Star Belgrade.
Group I: Salzburg, Marseille, Vitoria Guimaraes, Konyaspor.
Group J: Athletic Bilbao, Hertha Berlin, Zorya Luhansk, Ostersund.
Group K: Lazio, Nice, Zulte Waregem, Vitesse Arnhem.
Group L: Zenit St Petersburg, Real Sociedad, Rosenborg, Vardar.
Arsenal have been drawn in the same group as BATE Borisov, Cologne and Red Star Belgrade in the Europa League.