Chelsea's reward for seeing off Steaua Bucharest is a tie with Russian side Rubin Kazan, who battled past Levante in the round of 16.
Tottenham, who eked past Inter on away goals after a 4-1 defeat at San Siro, will be in for another rough ride against Swiss outfit Basel, fresh from eliminating Zenit St Petersburg.
After knocking out Anzhi Makhachkala with a last-minute goal from Papiss Cisse, Newcastle face another stern test in Benfica.
Turkish side Fenerbahce were drawn against Serie A outfit Lazio to complete the draw.
The four first legs will take place on April 4, with the return matches one week later.
The Europa League semi-final draw will be made on Friday April 12, with ties to be played on April 25 and May 2.
This year's final will be held at the Amsterdam ArenA on May 15.