Tottenham will play Manchester City in the Champions League quarter-finals, while Manchester United have been drawn against Barcelona.
Last year's beaten finalists Liverpool will play Porto, and Ajax will face Juventus in the other ties.
The semi-final draw was also made and Manchester United will meet Liverpool if both win their last-eight ties.
The quarter-final first legs take place on 9 April and 10 April. The semi-finals start on 30 April and 1 May.
City and United were both drawn away in the first leg of their ties, but they are not allowed to play at home on the same day or even consecutive nights.
Therefore, as United finished lower in the Premier League last season, their first leg will now be at Old Trafford, with the second leg at the Nou Camp.
The Champions League final takes place on 1 June at Madrid's 68,000-capacity Wanda Metropolitano, home of Atletico Madrid.
|Ajax v Juventus (April 10 at Johan Cruijff Arena, April 16 at Allianz Stadium)|
|Liverpool v Porto (April 9 at Anfield, April 17 at Estadio do Dragao)|
|Tottenham v Manchester City (April 9 at Spurs' stadium, April 17 at Etihad)|
|Barcelona v Manchester United (April 10 at Old Trafford, April 16 at Nou Camp)|
|Tottenham/Manchester City v Ajax/Juventus|
|Barcelona/Manchester United v Liverpool/Porto|
Premier League leaders Manchester City will face Spurs three times in 11 days.
Their quarter-final first-leg will likely be one of Spurs' first games at their new stadium on 9 April, before the return leg on 17 April and then their Premier League encounter at Etihad Stadium on 20 April.
Manchester United's draw sees a return to the Nou Camp for interim manager Ole Gunnar Solskjaer, 20 years after he scored a dramatic injury-time winner at the stadium in their 2-1 win over Bayern Munich in the 1999 Champions League final.
'Barcelona still favourites to win'
Simon Gleave, head of sports analysis, Gracenote
The top four remaining teams - Barcelona, Juventus, Manchester City and Liverpool - according to the Euro Club Index all avoided each other in the draw. Those four are therefore the favourites to progress to the semi-finals.
Juventus are estimated to have an 85% chance of knocking out Ajax and are the most likely to reach the last four. Barcelona have 78% chance of getting past Manchester United, and Manchester City have 71% chance of eliminating Tottenham Hotspur. Liverpool - FC Porto is the tightest looking of the four quarter-finals with Liverpool the favourites (68%) to go through.
Barcelona remain favourites to win the Champions League (38%), Juventus have a 24% chance of ending the season as the winners of the competition, Manchester City are third favourites on 19% and Liverpool come next on 10%. The chance of an English team winning the competition has dropped slightly to 35%.
Ajax v Juventus
Ajax are the first Dutch side to reach the Champions League quarter-finals since PSV Eindhoven in 2006-07.
They have the youngest starting XI in the competition and stunned Real Madrid with a 4-1 victory in the Spanish capital to reach the quarter-finals and end Los Blanos' 1,011-day reign as European champions.
Cristiano Ronaldo, who won the last three Champions League titles with Real, scored a hat-trick as Juventus overturned a 2-0 first-leg deficit against Atletico Madrid.
The Italians are unbeaten in their last 10 meetings with Ajax, winning five of the last six matches between the sides.
Head to head: Played: 12; Ajax: 2; Drawn: 4; Juventus 6
Liverpool v Porto
Liverpool, who lost the final 3-1 to Real Madrid last May, beat Bayern Munich on Wednesday to reach the last eight, while Portuguese champions Porto beat Roma.
It will be a repeat of last season's last-16 tie, which Jurgen Klopp's side won 5-0 in aggregate.
Porto have lost their last five two-legged knockout ties against English clubs and have not beaten English opposition in a knockout tie since Jose Mourinho's side eliminated Manchester United in the 2003-04 Champions League en route to lifting the trophy.
Head to head: Played: 6; Liverpool: 3; Drawn: 3; Porto: 0
Tottenham v Manchester City
Spurs reached the quarter-finals for the first time since 2011 with a 4-0 aggregate victory over Borussia Dortmund.
City eased into the last eight with a 7-0 home win over Schalke, winning 10-2 on aggregate.
City have lost each of their four games against English opponents in European competition - twice against Chelsea in 1971 and twice against Liverpool in last season's Champions League quarter-finals.
Head to head: First European meeting
Barcelona v Manchester United
Five-time European champions Barcelona thrashed Lyon 5-1 in midweek to reach the quarter-finals, while United became the first team in Champions League and European Cup history to overcome a 2-0 home first-leg deficit.
Marcus Rashford scored a 94th-minute penalty as they beat Paris St-Germain 3-1.
United have won just one of their eight European Cup/Champions League meetings with Barcelona, losing both of their last two encounters in the 2009 and 2011 finals.
Barcelona forward Lionel Messi has scored 22 Champions League goals against English clubs; more than any other player in the competition.
Head to head: Played: 11; United: 3; Drawn: 4; Barcelona: 4
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