Manchester City will play Barcelona in the Champions League round of 16, while neighbors Manchester United have been drawn against Olympiakos.
Victors over fellow German side Borussia Dortmund at Wembley in the 2012-13 final, the reigning Bundesliga champions return to London to tackle Arsene Wenger's high-flying Gunners at the Emirates Stadium in the first leg of a spring showdown.
Real Madrid are targeting a 10th European Cup and must get past Schalke, whom they visit in February, while last season's runners-up Dortmund are in Russia to meet Zenit St Petersburg.
Barcelona, winners in 2009 and 2011, travel to big-spending Manchester City, who finished second to Bayern in Group D after stunning the Germans with a 3-2 win in the last pool game.
Seven-time European champions AC Milan welcome ambitious Spaniards Atletico Madrid to the San Siro and cash-rich Paris Saint-Germain head to Germany to face Group A runners-up Bayer Leverkusen.
Didier Drogba prepares to meet his old Chelsea team-mates as Galatasaray host the Blues in Istanbul and Greek champions Olympiacos entertain English opposition in the form of 2008 winners Manchester United.
The first legs will be played on February 18-19 and 25-26 with the return fixtures scheduled for March 11-12 and 18-19.
The final takes place at Benfica's Estadio da Luz on May 24.
Full draw:
Manchester City v Barcelona
Olympiakos v Manchester United
AC Milan v Atletico Madrid
Bayer Leverkusen v Paris Saint-Germain
Galatasaray v Chelsea
Schalke v Real Madrid
Zenit St Petersburg v Borussia Dortmund
Arsenal v Bayern Munich
