Scottish champions Celtic will take in a tricky test against La Liga heavyweights Valencia.
Other notable ties include Lazio locking horns with Sevilla and Galatasaraytaking on Benfica.
Inter will try to make their way past Rapid Wien, Napoli tackle FC Zurich and Sporting meet Villarreal.
Arsenal will be looking to make it one step further than they managed in 2017-18, when they fell at the semi-final stage to eventual winners Atletico Madrid.
Unai Emery is now at the Gunners helm and he boasts an impressive record in the competition, having claimed the trophy in three successive years with Sevilla between 2014 and 2016.
He will be hoping to emulate the success Arsene Wenger enjoyed against BATE last season, when Arsenal secured a 4-2 victory away from home in the group stage and a 6-0 win at Emirates Stadium.
Chelsea, meanwhile, are looking to recapture a piece of silverware they last lifted back in 2013.
Maurizio Sarri will be determined to end his debut campaign with a major honour after being charged with the task of forcing the Blues back into contention for top prizes.
Both the Blues and London rivals Arsenal will also view the Europa League as a potential route into the Champions League, with the battle for top-four finishes in the Premier League set to leave some big sides disappointed.
Elsewhere, Celtic will be eager to prove that they can hold their own among the continental elite after edging out RB Leipzig at the group stage.
Brendan Rodgers’ side have not been as dominant domestically this term as they have been in recent years, but have the opportunity to put down a European marker against Valencia.
Los Che are enduring a testing 2018-19 campaign, as they sit 14th in the Spanish top-flight, but boast plenty of pedigree and may need the Europa League to salvage their season.
Inter and Napoli both boast the firepower to go deep into the competition, with the Serie A rivals having tumbled out of the Champions League.
The likes of Mauro Icardi and Dries Mertens will be looking to inspire their respective challenges.
Lazio are also in the mix, but have been handed the toughest draw of the Italian representatives as they prepare to take on La Liga high-fliers and Europa League experts Sevilla.
There are plenty of other intriguing contests to catch the eye, with leading sides from Germany, France, Turkey, Russia and Portugal all seeking to force their way into contention for a prestigious prize.
The first legs of the fixtures in the round of 32 will take place on February 14, with the return dates being staged a week later.
Europa League last 32 draw in full:
1. Olympiacos vs Dynamo Kiev
2. BATE Borisov vs Arsenal
3. Malmo vs Chelsea
4. Viktoria Plzen vs Dinamo Zagreb
5. Club Brugge vs Red Bull Salzburg
6. Rapid Wien vs Inter
7. Slavia Prague vs Genk
8. Krasnodar vs Bayer Leverkusen
9. FC Zurich vs Napoli
10. Shakhtar Donetsk vs Eintracht Frankfurt
11. Celtic vs Valencia
12. Rennes vs Real Betis
13. Lazio vs Sevilla
14. Fenerbahce vs Zenit
15. Sporting vs Villarreal
16. Galatasaray vs Benfica
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