Bayern and United will be favourites to advance from Group A which also includes Danish champions FC Copenhagen and Galatasaray, the Turkish champions.
Newcastle are appearing in the Champions League for the first time in 20 years and their lack of recent pedigree in Europe's elite club competition meant they were left lurking dangerously among the sides in pot four for the draw.
Having held on to Kylian Mbappe, French champions PSG will be expected to advance to the last 16 but Newcastle will hope to finish ahead of Dortmund and a Milan team that got to the semi-finals last season.
Real Madrid, the record 14-time champions who won the trophy in 2022, were drawn with Italian champions Napoli in Group C, which also features Braga of Portugal and Champions League debutants Union Berlin.
Scottish champions Celtic will face Feyenoord, Atletico Madrid and Lazio in Group E.