Everton will face Lille, Wolfsburg and FC Krasnodar in the Europa League groups stages as they begin their first European campaign since 2009-10.
Tottenham have been drawn against Besiktas, Partizan Belgrade and Greek side Asteras Tripolis after beating AEL Limassol in their qualifier.
Scottish champions Celtic meet Salzburg, Dinamo Zagreb and Romanians FC Astra.
This season's winners qualify for next year's Champions League.
After qualifying for the competition by finishing fifth in the Premier League last season, Roberto Martinez's Everton will face each of their Group H opponents for the first time.
Lille finished third in France's Ligue 1 and Wolfsburg came fifth in Germany's Bundesliga, while Krasnodar finished fifth in the Russian league.
Tottenham were knocked out at the quarter-final stage in 2013 and were beaten in the last 16 by Benfica last season.
They beat Group C rivals Besiktas in the Uefa Cup in 2006 but have never met either Partizan Belgrade or Asteras Tripolis.
Celtic, who dropped into the Europa League after their Champions League exit against Maribor, were beaten in a Champions League qualifier by Dinamo Zagreb in 1998.
Holders Sevilla line up in Group G alongside Standard Liege and Feyenoord, while three-time winners Inter Milan are in Group F.
The group phase begins on Thursday, 18 September and the final of this season's competition takes place at Stadion Narodowy in Warsaw on 27 May, 2015.
|Europa League groups|
|FC Zurich||Apollon Limassol|
|FC Copenhagen||Club Bruges|
|Partizan Belgrade||Asteras Tripolis|
|Dinamo Zagreb||FC Astra|
|Estoril Praia||Dynamo Moscow|
|Inter Milan ||FC Dnipro|
|St Etienne||Qarabag FK|
|Young Boys||Slovan Bratislava|
|Dynamo Kiev||Steaua Bucharest|
|Legia Warsaw||KSC Lokeren|