Liverpool will visit Russia after being drawn in the same group as Rubin Kazan, while Tottenham must go to Azerbaijan to face Qarabag in the Europa League.
The Reds also face Bordeaux from France and FC Sion of Switzerland.
As well as Qarabag, Tottenham must play Belgian side Anderlecht and Monaco from the French league.
Celtic, who missed out on a place in the Champions League group stage, meet Dutch giants Ajax, Turkey's Fenerbahce and Norwegian outfit Molde.
Each team will play six games in the group stage, with the first match day taking place on 17 September.
Group A: Ajax, Celtic, Fenerbahce, Molde
Group B: Rubin Kazan, Liverpool, Bordeaux, FC Sion
Group C: Borussia Dortmund, Paok Thessaloniki, Krasnodar, Gabala
Group D; Napoli, Club Brugge, Legia Warsaw, Midtjyllland
Group E: Villarreal, Viktoria Plzen, Rapid Vienna, Dinamo Minsk
Group F: Marseille, Braga, Slovan Liberec, Groningen
Group G: Dnipropetrovsk, Lazio, St-Etienne, Rosenborg
Group H: Sporting Lisbon, Besiktas, Lokomotiv Moscow, Skenderbeu
Group I: Basel, Fiorentina, Lech Poznan, Belenenses
Group J: Tottenham, Anderlecht, Monaco, Qarabag
Group K: Schalke, Apoel Nicosia, Sparta Prague, Asteras Tripolis
Group L: Athletic Bilbao, AZ Alkmaar, Augsburg, Partizan Belgrade
Lowdown on Liverpool's opponents
Rubin Kazan: Finished fifth in the Russian Premier League last season. They started this season's competition in the qualifying rounds, defeating Sturm Graz of Austria and FK Rabotnicki of Macedonia. The distance from Liverpool to Kazan is 2,500 miles.
Bordeaux: Uefa Cup runners-up in 1995-96, Bordeaux finished sixth in France's top-flight last season. Manager Willy Sagnol, 38, won the Champions League with Bayern Munich as a defender.
FC Sion: Last season's Swiss Cup winners. Manager Didier Tholot had a loan spell at Walsall as a player in 1998.
|17 September: Bordeaux (A)||5 November: Rubin Kazan (A)|
|1 October: Sion (H)||26 November: Bordeaux (H)|
|22 October: Rubin Kazan (H)||10 December: Sion (A)|
Lowdown on Tottenham's opponents
Anderlecht: Finished third in the Belgium's top flight last season. The two clubs met in the Uefa Cup final in 1984, when Spurs won on penalties after the two-legged final ended 2-2 on aggregate.
Monaco: Finished third in the French League last season. Their squad includes midfielder Mario Pasalic, on loan from Chelsea, and former Chelsea defender and three-time Premier League winner Ricardo Carvalho.
Qarabag: Winners of the Azerbaijan Premier Division last season, they play their home games in Baku, the country's capital. Most of their squad is home grown, although there are a number of Brazilian players at the club. One of them is forward Reynaldo, whose former sides include Anderlecht. The distance from Tottenham to Baku is 2,900 miles.
|17 September: Qarabag (H)||5 November: Anderlecht (H)|
|1 October: Monaco (A)||26 November: Qarabag (A)|
|22 October: Anderlecht (A)||10 December: Monaco (H)|
Lowdown on Celtic's opponents
Ajax: Four-time champions of Europe and Dutch league runners-up last season. Their squad includes former Everton and Fulham defender John Heitinga. Manager Frank de Boer had a spell at Rangers as a player.
Fenerbahce: Runners-up in Turkey's top-flight last season. Their squad includes a couple of former Manchester United players in the shape of forward Robin van Persie and winger Nani.
Molde: This is the first time the Norwegian club has competed in the group stages of the Europa League since 2012-13. Their squad includes former Manchester United youth midfielder Etzaz Hussain, 22, and United States international winger Josh Gatt. Defender Vegard Forren was on Southampton's books before joining Molde in 2013.
|17 September: Ajax (A)||5 November: Molde (H)|
|1 October: Fenerbahce (H)||26 November: Ajax (H)|
|22 October: Molde (A)||10 December: Fenerbahce (A)|