In the last eight, Chelsea will take on Spanish champions Real Madrid for the second-consecutive season, Manchester City will face Atletico Madrid - who knocked out Man United - and Liverpool were drawn against Benfica.
Villarreal go up against Bayern Munich in the other quarter-final tie.
The three Premier League clubs are among the favourites for European glory this season and managed to avoid each other in the quarter-final draw.
However, Chelsea and Man City will meet in the semi-finals if they progress as their two ties were drawn together for the last four.
Meanwhile, Benfica or Liverpool will face Villarreal or Bayern Munich in the next round.
Liverpool overcame Inter Milan with a 2-1 aggregate victory in the last-16, while City and Chelsea made light work of Sporting Lisbon and Lille respectively.
The draw throws up a number of interesting sub-plots, such as ex-Chelsea manager and current Real Madrid boss Carlo Ancelotti returning to Stamford Bridge, plus a clash between old rivals and opposite ideologies as City's Pep Guardiola and Atletico's Diego Simeone face off.
Defending champions Chelsea face added complications ahead of next months's quarter-finals due to EU sanctions imposed on owner Roman Abramovich.
The Blues will have to play home legs behind closed doors and away games without travelling supporters unless a new owner is put in place beforehand.
Thomas Tuchel's side were originally due to host Real Madrid in the first leg, but the matches have been reversed to prevent Real and Atletico playing home fixtures on the same night.
Quarter-finals ties will be played on April 5/6 and April 12/13, before the semi-finals on April 26/27 and May 3/4.
The final will take place at the Stade de France in Paris on May 28 after it was moved from St Petersburg following Russia's invasion of Ukraine.