Manchester United face a 6,000-mile round trip to play Astana in Kazakhstan in the Europa League.
The 2017 winners will also take on Partizan Belgrade and AZ Alkmaar, while Wolves - playing in Europe for the first time since 1980 - face Besiktas, Braga and Slovan Bratislava
Arsenal, who lost to Chelsea in last season's final, have drawn Eintracht Frankfurt, Standard Liege and Vitoria.
Celtic will face Lazio, while Rangers are in a tough group with Porto.
It is a difficult assignment for both Scottish clubs, with Neil Lennon's Celtic also taking on Dan Petrescu's Romanian champions Cluj, who knocked them out of Champions League qualifying, and French top-flight side club Rennes.
Rangers, managed by Steven Gerrard, have also been drawn against Dutch Eredivisie club Feyenoord and Swiss side Young Boys.
Premier League side Manchester United have arguably one of the more testing draws, including a nine-hour-plus flight to play Astana.
European football's governing body Uefa has ordered Serbian club Partizan Belgrade to play two matches behind closed doors after their qualifying game against Turkish club Yeni Malatyaspor was marred by supporters' "racist behaviour".
AZ Alkmaar, United's third Group L opponents, saw part of the roof at their ground collapse earlier in August.
Arsenal face German top-flight opposition in Eintracht Frankfurt, who lost on penalties to Chelsea in the semi-finals last season.
Frankfurt are the ninth German club that the Gunners have encountered in Europe, while Liege who finished third in the Belgian First Division last term are managed by former Belgium goalkeeper Michel Preud'homme.
Emery's side who are playing in competition for the third consecutive season will also travel to Portugal to face Vitoria in Guimaraes.
Wolves have already come through three ties just to reach the group stage, including beating Serie A side Torino 5-3 on aggregate in the play-offs.
And Nuno Espirito Santo's side will visit Turkey, Portugal and Slovakia in Group K.
Group stage draw in full:
Group A: Sevilla, Apoel Nicosia, Qarabag, F91 Dudelange
Group B: Dynamo Kiev, FC Copenhagen, Malmo, Lugano
Group C: Basel, Krasnodar, Getafe, Trabzonspor
Group D: Sporting Lisbon, PSV Eindhoven, Rosenborg, Lask
Group E: Lazio, Celtic, Rennes, Cluj
Group F: Arsenal, Eintracht Frankfurt, Standard Liege, Vitoria
Group G: Porto, Young Boys, Feyenoord, Rangers
Group H: CSKA Moscow, Ludogorets, Espanyol, Ferencvaros
Group I: Wolsfburg, Gent, Saint-Etienne, Olexandriya
Group J: Roma, Borussia Monchengladbach, Istanbul Basaksehir, Wolfsberger AC
Group K: Besiktas, Braga, Slovan Bratislava, Wolves
Group L: Manchester United, FC Astana, Partizan Belgrade, AZ Alkmaar