Chelsea will face Barcelona and Tottenham have been drawn against Juventus in the Champions League last-16 stage.
A record five English teams progressed from the group stage this season.
Premier League leaders Manchester City will take on Basel, Manchester United will play against Sevilla and Liverpool will see if they can surpass Portugal's Porto.
The group winners will be away in the round of 16 first legs on 13/14 and 20/21 February, and at home in the return matches on 6/7 and 13/14 March.
The final will take place in Kiev on 26 May.
Champions League last-16 draw
Juventus v Tottenham (13 February and 7 March)
Basel v Manchester City (13 February and 7 March)
Porto v Liverpool (14 February and 6 March)
Sevilla v Manchester United (21 February and 13 March)
Real Madrid v PSG (14 February and 6 March)
Shakhtar Donetsk v Roma (21 February and 13 March)
Chelsea v Barcelona (20 February and 14 March)
Bayern Munich v Besiktas (20 February and 14 March)