Manchester United face a gruelling Europa League group-stage trip to Kazakhstan while Celtic have a rematch against Cluj, who eliminated them from the Champions League.
United have been drawn in Group L and will face Astana of Kazakhstan, Serbian side Partizan Belgrade and AZ Alkmaar of the Netherlands.
United will have to endure a 6,000-mile round trip to Astana, who are based in Kazakhstan's capital city Nur-Sultan, and fans taking the journey can expect a flight time of at least nine hours one-way.
There are fewer travel issues for last season's runners-up Arsenal who take on Eintracht Frankfurt, Standard Liege and Portuguese side Vitoria in Group F.
Arsenal were defeated in May's final by Chelsea in Baku, but they will be expected to progress from the group despite it containing last season's semi-finalists Frankfurt.
The other Premier League side in the draw Wolves will play Besiktas, Braga and Slovan Bratislava in Group K in their first European campaign since 1980.
Wolves reached the group stages perfectly, winning all six of their qualifying matches including a 5-3 aggregate win over Italian side Torino.
Scottish champions Celtic will get a chance for revenge against their Champions League conquerors Cluj of Romania with both teams drawn together in Group E alongside Lazio and Rennes.
Neil Lennon's side were stunned by the Romanian champions this month as they lost 5-4 on aggregate in the third qualifying round of the Champions League.
Rangers have been given a tough group as they will face Porto, Feyenoord and Young Boys of Switzerland in Group G.
Steven Gerrard's side have been ordered to close a 3,000-seat section for their first Europa League group game at Ibrox as punishment for sectarian chanting against Legia Warsaw last week.
One of the bookmakers' favourites for the competition, Sevilla, have been drawn to face Azerbaijan side Qarabag who defeated Linfield in the play-off round.
The final of this season's Europa League takes place in the Polish city of Gdansk on 27 May.
Europa League draw in full
Group A: Sevilla, APOEL, Qarabag, Dudelange
Group B: Dynamo Kiev, 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: Wolfsburg, Gent, Saint-Etienne, Oleksandriya
Group J: Roma, Borussia Monchengladbach, Istanbul Basaksehir, Wolfsberger
Group K: Besiktas, Braga, Wolves, Slovan Bratislava
Group L: Manchester United, Astana, Partizan Belgrade, AZ Alkmaar
2019-20 Europa League group stage selected fixtures
Rennes vs Celtic
Eintracht Frankfurt vs Arsenal
Rangers vs Feyenoord
Wolves vs Braga
Manchester United vs Astana
Celtic vs Cluj
Arsenal vs Standard Liege
Young Boys vs Rangers
Besiktas vs Wolves
AZ Alkmaar vs Manchester United
Celtic vs Lazio
Arsenal vs Vitoria
Porto vs Rangers
Slovan Bratislava vs Wolves
Partizan Belgrade vs Manchester United
Lazio vs Celtic
Vitoria vs Arsenal
Rangers vs Porto
Wolves vs Slovan Bratislava
Manchester United vs Partizan Belgrade
Celtic vs Rennes
Arsenal vs Eintracht Frankfurt
Feyenoord vs Rangers
Braga vs Wolves
Astana vs Manchester United
Cluj vs Celtic
Standard Liege vs Arsenal
Rangers vs Young Boys
Wolves vs Besiktas
Manchester United vs Alkmaar