Arsenal will face BATE Borisov, Cologne and Red Star Belgrade, while Everton take on Lyon, Atalanta and Apollon Limassol.
Both English sides face difficult tasks to advance to the knockout stages when the group phase begins on September 14.
It is the first time in 20 years that Arsenal have started a European campaign in the Europa League.
The Gunners had advanced to the knockout stages of the Champions League but lost in the first knock-out round in the last seven seasons and failed to qualify for the tournament through the Premier League in 2016-17.
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Everton, who completed their play-off victory over Hajduk Split of Croatia on Thursday, are in Europe for the first time since 2009-10.
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Everton secured their place in the Europa League after beating Hajduk Split
Manchester United won the trophy in May to qualify for the Champions League.
United and France midfielder Paul Pogba was named Europa League Player of the Season for 2016-17, ahead of team-mates Zlatan Ibrahimovic and Henrikh Mkhitaryan.
The 48-team draw for this season's competition included Sweden's Ostersund, managed by Englishman Graham Potter.
Ostersund will play Spain's Athletic Bilbao, Germany's Hertha Berlin and Zorya Luhansk of Ukraine in Group J.
Europa League draw in full
Group A: Villarreal, Maccabi Tel-Aviv, Astana, Slavia Prague
Group B: Dynamo Kiev, Young Boys, Partizan Belgrade, Skenderbeu
Group C: Braga, Ludogorets, Hoffenheim, Istanbul Basaksehir
Group D: AC Milan, Austria Vienna, NK Rijeka, AEK Athens
Group E: Lyon, Everton,Atalanta, Apollon Limassol
Group F: FC Copenhagen, Lokomotiv Moscow, Sheriff Tiraspol, FC Zlin
Group G: Viktoria Plzen, Steaua Bucharest, 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, Ostersunds
Group K: Lazio, Nice, Zulte Waregem, Vitesse Arnhem.
Group L: Zenit, Real Sociedad, Rosenborg, Vardar Skopje