Premier League leaders Liverpool will face Sparta Prague in the last 16 of the Europa League, while Brighton face another glamour tie against Roma.
The Reds will travel to the Czech capital for the first leg on 7 March, before a return at Anfield a week later in a competition Liverpool have won three times in the past.
Brighton's maiden European campaign takes them to the Italian capital after they topped Group B containing Marseille, Ajax and AEK Athens.
Europa Conference League holders West Ham face German team Freiburg, while Rangers are up against two-time European champions Benfica from Portugal.
Former Republic of Ireland defender John O'Shea was in Nyon to help make the draw. The Europa League final will take place at the Aviva Stadium in Dublin on 22 May.
In the Europa Conference League, Aston Villa were pitted against Dutch giants Ajax in the last 16.
Villa progressed as Group E winners and now face the Amsterdam club, who have been champions of Europe four times.
Ajax signed England midfielder Jordan Henderson last month, although he did not feature as they beat Norwegian side Bodo Glimt in extra-time to progress from the knockout play-off round.
The first leg will be played in Amsterdam on 7 March, with the return at Villa Park on 14 March. On the same dates, Robbie Keane's Maccabi Tel Aviv will face off with Olympiakos for a place in the quarters.
The Conference League final takes place in Athens on 29 May.
Europa League last-16 draw
Sparta Prague v Liverpool
Marseille v Villarreal
Roma v Brighton
Benfica v Rangers
Freiburg v West Ham
Sporting Lisbon v Atalanta
AC Milan v Slavia Prague
Qarabag v Bayer Leverkusen
Europa Conference League last-16 draw
Servette v Viktoria Plzen
Ajax v Aston Villa
Molde v Club Bruges
Union Saint-Gilloise v Fenerbahce
Dinamo Zagreb v PAOK
Sturm Graz v Lille
Maccabi Haifa v Fiorentina
Olympiakos v Maccabi Tel Aviv
