Antonio Conte's team, whose stadium will host the final in Turin in May, will travel to France for the first leg on April 3 with the return a week later.
The twice European champions won the old UEFA Cup three times and the Cup Winners' Cup once.
Benfica, beaten finalists last season, were drawn against Dutch club AZ Alkmaar while their compatriots Porto, who knocked out Napoli in the previous round, face Sevilla.
In the other tie, Basel meet Valencia with the Swiss side, beaten semi-finalists last season, at home in the first leg.
Basel could still face disciplinary action after Thursday's match at Salzburg was interrupted in the first half for 12 minutes when their fans hurled plastic bottles and cigarette lighters at an opposing player.
Europa League quarter-finals in full:
- Sports & Recreation
- AZ Alkmaar
- Antonio Conte
- Champions League