The draw, which took place in Nyon on Monday, produced several intriguing clashes with Premier League side Tottenham facing a difficult tie with Fiorentina, while Zenit take on Eredivisie leaders PSV.
Other notable encounters see defending champions Sevilla, attempting to win the competition for a fourth time, face Bundesliga outfit Borussia Monchengladbach and Everton tackle Young Boys of Switzerland.
First leg ties will be played on March 12, with the return fixtures taking place a week later on March 19.
The Europa League offers Brendan Rodgers' Liverpool side the chance to bounce back from a disappointing Champions League campaign, in which they won just one of their six group matches.
Against Besiktas, the Merseyside club will meet a familiar foe in Demba Ba, who capitalised on a slip from Steven Gerrard to help former club Chelsea beat Liverpool 2-0 at Anfield last April - severely denting their Premier League title hopes.
Roma are also aiming to quickly forget their experience of Europe's top table.
Rudi Garcia's men faced a final game showdown with Manchester City on matchday six, but a 2-0 defeat at Stadio Olimpico meant they dropped into Europe's secondary competition.
Inter, who won the trophy for a third time in 1998, have faced difficulty in Serie A this season and currently sit 12th after 14th matches. They face Scottish champions Celtic in a repeat of the 1967 European Cup final - won 2-1 by the men from Glasgow.
La Liga outfit Sevilla defeated Primeira Liga champions Benfica 4-2 on penalties in May's final in Turin to add to their victories in 2006 and 2007.
Two-time victors Gladbach are sure to pose a difficult proposition with Lucien Favre's side occupying fourth spot in the Bundesliga.
Draw in full:
Young Boys v Everton
Torino v Athletic Bilbao
Sevilla v Borussia Monchengladbach
Wolfsburg v Sporting Lisbon
Ajax v Legia
AaB v Club Brugge
Anderlecht v Dinamo Moscow
Dnipro v Olympiacos
Trabzonspor v Napoli
Guingamp v Dynamo Kiev
Villarreal v Red Bull Salzburg
Roma v Feyenoord
PSV v Zenit
Liverpool v Besiktas
Tottenham v Fiorentina
Celtic v Inter
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