Seven-times champions AC Milan will face Arsenal in one of two Italian-English ties with Napoli, in the knockout rounds for the first time, facing Chelsea.
Arsenal have advanced on all eight occasions when they have met Italian teams in the knockout rounds.
Real Madrid, seeking to become European champions for a tenth time, were given a trip to icy Russia in February when they drew CSKA Moscow - something their arch-rivals Barcelona were happy to avoid.
"We got Bayer, well, perfect. All the teams have their positives and negatives. Like all things in life, you can focus on the rough and the smooth," said Barcelona president Sandro Rosell.
"With the Russian teams, for example, we preferred not to get one of them due to the plane trip, the fact you have to travel a day earlier and the cold, but, on the other hand they are in pre-season."
Barca's sporting director Andoni Zubizarreta told reporters: "German teams are always tough. I have always liked German football. They have stadiums that are full of passion, emotion and young people and it seems to me an excellent place to go and play."
Bayer Leverkusen sports director Rudi Voller said: "We are playing against the defending champions and are of course the clear outsiders.
"Both for our fans and young players, this is a dream draw... everyone must play their best and Barcelona could have a bad day."
Bayern, who beat FC Basel home and away in last year's group stage, refused to take Basel lightly after the Swiss champions qualified at Manchester United's expense.
"If we remain focused and play with full force then we have a good chance to move into the quarter-finals," said Bayern CEO Karl-Heinz Rummenigge on the club website. "But please, no underestimating Basel."
This season's final will be played in Munich's Allianz Arena in May.
Surprise packages APOEL Nicosia, the first Cypriot club to reach this stage, will play Olympique Lyon.
The other matches pitch Zenit St Petersburg against Benfica, who were last European champions 50 seasons ago, and 1993 champions Olympique Marseille against three-times winners Inter Milan.
Real admitted that conditions in Russia would be a worry.
"We have to be careful, the temperatures will be low in Moscow on those dates, we are not used to that, it could be a problem," director and former striker Emilio Butragueno told Reuters.
"It's an element that can have an impact on that game. The artificial pitch will also be a novelty."
Napoli's home record could be a worry for Chelsea as they have not been beaten in their San Paolo stadium in European competition for 17 years.
"It will be difficult, we've already seen from their group perfo
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