City will play Barcelona in the Champions League round of 16, while neighbours United have been drawn against Olympiakos.
Chelsea must take on Galatasaray who dramatically edged out Juventus last week, with Premier League leaders Arsenal drawn against current holders Bayern Munich.
Full draw:
Manchester City v Barcelona
Olympiakos v Manchester United
AC Milan v Atletico Madrid
Bayer Leverkusen v Paris Saint-Germain
Galatasaray v Chelsea
Schalke v Real Madrid
Zenit St Petersburg v Borussia Dortmund
Arsenal v Bayern Munich