Liverpool face Russian giants Zenit St Petersburg, who won the trophy in 2008, while last year's Champions League winners Chelsea were rewarded with a trip to Sparta Prague in their first leg.
Newcastle must negotiate Metalist Kharkiv in Ukraine, while Spurs are punished for coming second in their group with a tough tie against French giants Lyon.
Tottenham goalkeeper Hugo Lloris, who joined from Lyon this season, will look forward to the tie against his old team-mates.
"It was destiny, it will be certainly very emotional for him," said Lyon manager Remi Garde, who used to play for Tottenham's London rivals Arsenal.
"It will not be easy. Tottenham seem to be improving by steps and I think Hugo has played a part in that because he has brought a lot of stability."
Defending champions Atletico Madrid also head east as they face Russia's Rubin Kazan, while Internazionale get Romania's CFR Cluj, who exited the Champions League from Manchester United's group.
The last 16 draw was also conducted, with Atletico facing a potential all-Spanish clash with Levante, while Chelsea could play Manchester City's Champions League conquerors Ajax.
Spurs ended up in Inter's side of the draw, while Liverpool would get FC Basel or Dnipro of Ukraine if they get past Zenit, whose fans caused controversy this week by releasing a charter demanding the club only sign white, heterosexual players.
Zenit reiterated their opposition to views advanced by the group of their supporters, insisting the Russian club was concerned only with the quality of players and not their ethnic origin, nationality or sexual orientation
Full last 32 draw:
BATE Borisov v Fenerbahce
Inter Milan v CFR Cluj
Levante v Olympiakos Piraeus
Zenit St Petersburg v Liverpool
Dynamo Kiev v Girondins Bordeaux
Bayer Leverkusen v Benfica
Newcastle United v Metalist Kharkiv
VfB Stuttgart v Racing Genk
Atletico Madrid v Rubin Kazan
Ajax Amsterdam v Steaua Bucharest
Basel v Dnipro Dnipropetrovsk
Anji Makhachkala v Hanover 96
Sparta Prague v Chelsea
Borussia Moenchengladbach v Lazio
Tottenham Hotspur v Olympique Lyon
Napoli v Viktoria Plzen
Teams listed first will play first legs at home.
* First legs to be played February 14, second legs February 21
Napoli/Viktoria Plzen v BATE Borisov/Fenerbahce
Bayer Leverkusen/Benfica v Dynamo Kiev/Bordeaux
Anji Makhachkala/Hanover 96 v Newcastle /Metalist Kharkiv
Stuttgart/Racing Genk v Borussia M./Lazio
Tottenham/Lyon v Inter Milan/CFR Cluj
Levante/Olympiakos v Atletico Madrid/Rubin Kazan
Basel/Dnipro v Zenit St Petersburg/Liverpool
Ajax/Steaua Bucharest v Sparta Prague/Chelsea
* First legs to be played March 7, second legs March 14