Arsenal will face Bayern Munich, Leicester City will play Sevilla and Manchester City are up against Monaco in the Champions League last 16.
The Gunners have played the German champions four times in the previous five campaigns and finished behind them in the group stage last season.
The Foxes, in their debut campaign, have a tough test against Europa League champions Sevilla.
Manchester City’s opponents Monaco beat Tottenham twice in Group E.
One of the other standout ties of the round puts Spanish champions Barcelona against French champions Paris St-Germain. Barca beat PSG in the quarter-finals en route to winning the title during the 2014-15 season.
Champions and La Liga leaders Real Madrid face Italian side Napoli, who are fourth in Serie A.
Manchester City v Monaco
Real Madrid v Napoli
Benfica v Borussia Dortmund
Bayern Munich v Arsenal
FC Porto v Juventus
Bayer Leverkusen v Atletico Madrid
Paris St-Germain v Barcelona
Sevilla v Leicester
(First legs to be played on 14 & 15 and 21 & 22 February 2017; second legs on 7 & 8 and 14 & 15 March)
‘The tide has got to turn’
Arsenal have been knocked out by Bayern in the three previous occasions they have met in the knockout stage.
Gunners club secretary David Miles told BT Sport: “We are through to the knockout stage for the 14th consecutive season which is testament to manager Arsene Wenger and the teams throughout that time.
“But the fans will think we have got the rough end of the draw again – at some stage the tide has got to turn and we will beat them.”
Bayern skipper Philipp Lahm tweeted: “Tough draw as Arsenal is in really good shape. Looking forward to seeing my former colleagues from the national team again!”
Manchester City director of football Txiki Begiristain said that Monaco should not be underestimated.
He added: “Monaco are playing probably the best football in France now.
“In the group of Tottenham and Bayer Leverkusen they were top. They have young players and a lot of talent. They play good football. It is a good draw.”
Analysis – progress is realistic
By chief football writer Phil McNulty
The Premier League’s three representatives in the last 16 of the Champions League have all been handed tough draws – but also ties that will offer them the realistic opportunity of progress.
Arsenal, reigning champions Leicester City and Manchester City could have been given easier opponents but there will also be guarded optimism surrounding the prospect of facing Bayern Munich, Sevilla and Monaco.
The Gunners are aiming to end a run of six successive exits at this stage and some may curse the draw that pairs them with Bayern.
It is not a comfortable reward for topping their group and they have suffered before against Bayern in this competition.
Leicester City will give anyone a tough time if they play with the intensity and power they showed in thrashing Manchester City.
Monaco’s displays in beating Tottenham home and away will have warned Manchester City manager Pep Guardiola about their quality, and he also has serious defensive issues to address.