The German giants and other clubs have learned their set of fixtures for the newly formed group stage of the 36-team competition.
Villa, who won the European Cup in 1982 against Bayern, also face Celtic, Monaco, RB Leipzig, Juventus, Club Brugge, Bologna and Young Boys.
Speaking about the draw, Bayern chief Dreesen said: “We're happy with the opponents we've been drawn against. I've just told Nasser Al-Khelaifi from PSG that we're almost like an old married couple in the Champions League, because we're always involved with each other. It’ll certainly be an exciting encounter. I'm happy that we have this game at home.
“For me personally, the encounter with Aston Villa is very appealing. The last time we played them was in the final 42 years ago.
“Most honestly, our first priority is the Bundesliga. But we have a dream of reaching the Champions League final in Munich.”
Bayern goalkeeper Manuel Neuer added: “They will be very exciting matches against extremely good opponents. But we're going into the new league phase confident of qualifying automatically. We want to show how we stand against the other teams."