Dethroned Champions League winners Chelsea host Russian club Rubin Kazan in their first leg on April 4 while Tottenham are at home the same night against Swiss outsiders Basel and Newcastle travel to former European champions Benfica.
Tottenham, who won the inaugural competition in 1972 when it was known as the UEFA Cup and added their last European trophy in the same tournament in 1984, will fancy their chances against Swiss champions Basel.
Newcastle head to Lisbon after scoring with the last kick of the match on Thursday to defeat Russian club Anzhi Makhachkala and face a Benfica side who are two points clear of Porto and unbeaten in 22 domestic matches this season.
The final last-eight tie features 1999 Cup Winners' Cup champions' Lazio against Fenerbache with the first leg to be played in Istanbul.
The final is set to be played at the Amsterdam Arena on Wednesday, May 15.
Matches to be played on April 4 and 11:
Chelsea (ENG) v Rubin Kazan (RUS)
Tottenham Hotspur (ENG) v Basel (SUI)
Fenerbahce (TUR) v Lazio (ITA)
Benfica (POR) v Newcastle (ENG)