Manchester City face Tottenham Hotspur in an all-Premier League clash, their first European meeting, while Cristiano Ronaldo’s Juventus meet Ajax Amsterdam, who are back in the last eight after a 16-year absence.
Five-times European champions Liverpool, the fourth English representatives and beaten finalists last year, will face Porto in a repeat of last year’s last-16 tie which they won 5-0 on aggregate.
The semi-final pairings were also made with Tottenham or City to face Ajax or Juventus and Manchester United or Barcelona to meet either Liverpool or Porto.
The draw had an unusual feel with neither Bayern Munich nor Real Madrid in the hat, the first time both European giants have failed to reach the last eight since 2005-06.
Five-times winners Barcelona, who are in the last eight for the 12th successive season, will be away in the first leg after UEFA switched the order to avoid United’s home match clashing with Manchester City, who host Spurs in their second leg.
Tottenham and City will meet three times in 10 days in April with a Premier League fixture following hot on the heels of their second leg.
Ajax, once a major European power who struggle to compete financially with clubs from bigger leagues, ousted Real Madrid in the last 16 and their tie against Juventus will be a repeat of the 1996 final, which the Serie A club won on penalties.
They also met in the final of the old European Cup in 1973 with the Dutch side winning 1-0.
Juventus are unbeaten in their last 10 games against Ajax, winning five of the last six.
Porto, who won the competition in 2004 under Jose Mourinho, are confident they can spring an upset after last year’s mauling.
Chelsea were the last English team to win the Champion League in 2012.
The two-legged quarter-finals take place on April 9-10 and 16-17.
The Europa League quarter-final draw. (Photo: UEFA)
Meanwhile, Napoli, chasing their first European title since Diego Maradona’s team won the old UEFA Cup in 1989, were drawn against Arsenal in the quarter-finals of the Europa League on Friday.
Rank outsiders Slavia Prague, who ousted Sevilla in thrilling style on Thursday, were rewarded with a tie against Chelsea, the other English Premier League team in the last eight.
Villarreal and Valencia were drawn together in an all-Spanish tie and Benfica will meet Eintracht Frankfurt, who eliminated Inter Milan with a 1-0 win at San Siro.
Arsenal or Napoli will meet Villarreal or Valencia in the semi-finals while Benfica or Eintracht play Slavia or Chelsea.