The Premier League champions were placed in Group B and will be happy to have avoided Real Madrid, and former United star Cristiano Ronaldo, who were among the second seeds.
Chelsea, beaten in the semi-finals last year by eventual winners Barcelona, were grouped with Porto, Atletico Madrid and Apoel Nicosia in Group D.
Premier League runners-up Liverpool face Lyon, Fiorentina and Debreceni in Group E and Arsenal tackle AZ Alkmaar, Olympiacos and Standard Liege in Group H.
Scottish champions Rangers were drawn against Sevilla, Stuttgart and Romanian champions and Champions League newcomers Unirea Urziceni in Group G.
Holders Barcelona will face Inter Milan, Dynamo Kiev and Rubin Kazan in Group F.
AC Milan were drawn against nine-times winners Real Madrid, Marseille and FC Zurich in Group C, and Bayern Munich were joined by Juventus, Bordeaux and Maccabi Haifa in Group A.