Arsenal will face Swedish side Ostersund 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.
Ostersund are managed by Englishman Graham Potter, who previously played for Birmingham City and West Brom.
Potter has taken the club from the fourth division to the Allsvenskan, the Swedish top tier, in six years.
The 42-year-old has earned comparisons with Roy Hodgson - who managed in Scandinavia - 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.
Bundesliga giants Borussia Dortmund, who on Sunday sacked their head coach Peter Bosz, will face Atalanta, while 2010 Europa League winners Atletico Madrid meet FC Copenhagen after failing to qualify for the knockout stages of the Champions League.
Lyon, who will host the competition's final on May 16, have been drawn against Villarreal in one of the standout ties of the last 32.
Elsewhere, seven-time European champions AC Milan will meet Ludogrets, Marseille face Braga and Lazio are drawn with Romanian side Steaua Bucharest.
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
Ostersund v Arsenal
Olympique Marseille v Braga