Manchester United have been drawn against holders Bayern Munich in the Champions League quarter-finals, while Chelsea face Paris St-Germain.
Spanish champions Barcelona play La Liga rivals Atletico Madrid and Real Madrid meet Borussia Dortmund.
The first legs will be played on 1-2 April, with the return matches on 8-9 April.
This year’s final is to be held at Benfica’s Estadio da Luz in Lisbon on 24 May.
United overturned a 2-0 deficit against Olympiakos to book their spot in the last eight, while Chelsea saw off Galatasaray.
The Premier League champions’ 3-0 second-leg win against the Greeks provided some much-needed relief for manager David Moyes and his players.
Now they will play German leaders Bayern, who remain favourites to retain their European title after defeating Arsenal 3-1 on aggregate.
It is a rematch of the 1999 Champions League final, when late goals from Ole Gunnar Solskjaer and Teddy Sheringham won the trophy for Sir Alex Ferguson’s side.
Bayern beat United on away goals in the 2009-10 quarter-finals, ending the English club’s hopes of reaching a third successive final.
“We can’t allow Manchester United’s current position in the Premier League table to affect our mindset for this game,” said Bayern skipper Philipp Lahm after Friday’s draw in Switzerland.
“We’ll travel to Manchester to play attacking football and score goals. I don’t think it matters if you play the away leg first.”
Premier League leaders Chelsea will travel to the French capital to play PSG in their first leg.
The Ligue 1 champions, with Sweden striker Zlatan Ibrahimovic as their spearhead, are eight points clear of nearest rivals Monaco as they aim to retain their domestic title.
Chelsea are unbeaten in their two previous Champions League meetings with PSG – in Blues boss Jose Mourinho’s first season at Stamford Bridge.
The west London club won 3-0 in Paris before a 0-0 home draw in the 2004-05 group stage.
Spanish leaders Real, with Cristiano Ronaldo and Gareth Bale in blistering form, brushed aside Schalke 9-2 on aggregate in the last 16 and now face German opposition again after being drawn against last season’s runners-up Dortmund.
Atletico Madrid, who are second in La Liga, are rewarded for a comfortable 5-1 aggregate win against seven-time European champions AC Milan with a tie against domestic rivals Barcelona.
The sides drew 0-0 in their league meeting at Atletico’s Vicente Calderon stadium in January