Arsenal will face Swedish side Ostersunds in the Europa League round of 32, while Celtic face Russian side Zenit St Petersburg.
The Gunners, seeded for the draw, avoided the likes of Borussia Dortmund and Napoli – who were both in the unseeded pot.
Ostersunds are managed by Englishman Graham Potter, who previously played for Birmingham City and West Brom.
Potter has taken from the fourth division to the top-ranked Allsvenskan in six years.
The 42-year-old has earned comparisons with Roy Hodgson – who himself managed in Scandinavia in his formative years – and this will be his first clash against English opposition.
Arsenal will play the first leg away in Ostersund in mid-February, before returning to the Emirates.
Celtic, also unseeded, will play the first leg of their tie against Zenit at home, before a trip to the Zenit Arena in Russia, which is one of the 2018 World Cup venues in Russia.
Zenit were last week ordered to partially close their stadium by UEFA for their next European game after fans displayed a banner praising former Bosnian Serb military leader Ratko Mladic during a 2-1 home win over Macedonian side Vardar Skopje in the Europa League last month.
Europa League round of 32:
Borussia Dortmund v Atalanta
Nice v Lokomotiv Moscow
FC Copenhagen v Atletico Madrid
Spartak Moscow v Athletic Bilbao
AEK Athens v Dynamo Kiev
Celtic v Zenit St Petersburg
Napoli v RB Leipzig
Red Star Belgrade v CSKA Moscow
Olympique Lyonnais v Villarreal
Real Sociedad v FC Salzburg
Partizan Belgrade v Viktoria Plzen
Steaua Bucharest v Lazio
Ludogorets v AC Milan
Astana v Sporting Lisbon
Ostersunds v Arsenal
Olympique Marseille v Braga