Going to Azerbaijan to play Qarabag on October 4 could be problematic for Arsenal forward Henrikh Mkhitaryan, who is Armenian.
There has been diplomatic tensions between Azerbaijan and Armenia over the Nagorno-Karabakh territory, with a ceasefire declared in 1994 after fighting erupted several years earlier.
BATE also lost in the play-off round for Europe's premier club competition, going down 6-2 on aggregate to PSV Eindhoven, while Vidi were beaten at the same stage by AEK.
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Chelsea are back in the Europa League for the first time since they won the competition in 2013.
Austrian champions Red Bull Salzburg came out of pot one, and they are joined by Bundesliga outfit RB Leipzig, who are also associated with the energy drink manufacturer, and Norwegian title holders Rosenborg. The club spent more than $200 million on players a year ago under new Chinese owners and failed to comply with UEFA rules monitoring transfer fees and wages.
Celtic have made their way into the Europa League after missing out on a third successive Champions League group stage appearance.
Cross-city rivals Rangers have the toughest-looking draw of the British quartet.
Steven Gerrard's men will return to Russian Federation to face Spartak Moscow in Group G, which also contains La Liga side Villarreal and Austrian's Rapid Vienna.
The first set of group fixtures take place on September 20.