"Our group is certainly the most difficult... But we accept it. We are up against three absolute top opponents," Dortmund CEO Hans-Joachim Watzke told the club's website.
"To survive in this group, you need exceptional performances, and that's exactly what we're hoping for from our team."
City captured their first European crown this year and Pep Guardiola's side should have few problems in making the last 16, having handed Leipzig a 7-0 thrashing in last year's tournament.
Record 14-time winners Real Madrid will play Serie A champions Napoli, Braga and Union Berlin in Group C. German heavyweights Bayern Munich take on Manchester United, FC Copenhagen and Galatasaray in Group A.
Last season's runners-up Inter Milan meet Benfica, RB Salzburg and Real Sociedad in Group D, while Europa League winners Sevilla and Arsenal were drawn together in Group B along with PSV Eindhoven and RC Lens.
The Champions League group stage will begin on September 19th and conclude on December 13th. The knockout stages begin in February, with the final taking place at London's Wembley Stadium in June.