Manchester United will take on St Etienne in the Europa League's round of 32, while Tottenham Hotspur will face Gent and Villarreal have been drawn against Roma.
United, who finished second in their group behind Fenerbahce, come up against a side sitting eighth in Ligue 1 as they attempt to win the trophy for the first time in their history.
The two sides have met twice before in the European Cup Winners' Cup in 1977, with United emerging victorious over the two legs with a 3-1 win.
Paul Pogba could come up against his older brother over the tie, with Florentin Pogba a defender for St Etienne.
Spurs' Champions League campaign ended in disappointment after they could only finish third in their group, but they will hope to make more of a mark on the Europa League this term, starting with their tie against Belgian side Gent.
Roma's reward for topping their group is a tricky tie against Villarreal.
Roma, who remained unbeaten throughout the group stage and who currently sit second in Serie A, have been drawn against a Villarreal side that finished second in their pool behind Osmanlispor and who lie sixth in La Liga.
Borussia Monchengladbach, who finished third behind Barcelona and Manchester City in their Champions League group, have been handed a tough test against Serie A club Fiorentina.
Hapoel Be'er Sheva, who qualified at the expense of Southampton and Inter Milan, will play Turkish club Besiktas.
ROUND OF 32 DRAW:
The first legs will take place on Feb. 16, with the second legs on Feb. 23.
The draw for the round of 16 will take place on Feb. 24.
Athletic Bilbao v Apoel Nicosia
Legia Warsaw v Ajax
Anderlecht v Zenit St Petersburg
Astra Giurgiu v Racing Genk
Manchester United v St Etienne
Villarreal v Roma
Ludogorets Razgrad v FC Copenhagen
Celta Vigo v Shakhtar Donetsk
Osmanlispor v Olympiakos
Gent v Tottenham Hotspur
Rostov v Sparta Prague
Krasnodar v Fenerbahce
Borussia Monchengladbach v Fiorentina
AZ Alkmaar v Lyon
Hapoel Be'er Sheva v Besiktas
PAOK Salonika v Schalke