Manchester United will play La Liga side Real Sociedad while Arsenal will face former champions PSV Eindhoven in the Europa League group stage.
Erik ten Hag’s side will also play FC Sheriff and Omonia Nicosia in Group E in what appears to be a favourable draw for the Red Devils.
Arsenal have also been drawn with Bodo/Glimt and FC Zurich in Group A.
Inaugural Europa Conference League winners Roma are in Group C with Real Betis, Ludogorets and HJK.
Group stage draw in full
Group A: Arsenal, PSV Eindhoven, Bodo/Glimt, FC Zurich
Group B: Dynamo Kyiv, Rennes, Fenerbahce, AEK Larnaca
Group C: Roma, Ludogorets, Real Betis, HJK Helsinki
Group D: Braga, Malmo, Union Berlin, Union Saint-Gilloise
Group E: Manchester United, Real Sociedad, FC Sheriff, Omonia Nicosia
Group F: Lazio, Feyenoord, FC Midtjylland, SK Sturm Graz
Group G: Olympiakos, Qarabag, Freiburg, Nantes
Group H: Red Star Belgrade, Monaco, Ferencvaros TC, Trabzonspor
Draw throws up familiar faces
Manchester United, who won the tournament in 2017, last played Real Sociedad in the group stage of the Champions League in 2013.
FC Sheriff are the Moldovan champions while Omonia Nicosia, from Cyprus, are managed by former Celtic boss Neil Lennon.
All three of Arsenal’s group-stage rivals dropped out of the Champions League qualifying phase.
PSV, who are managed by former Manchester United striker Ruud van Nistelrooy, lost to Rangers in the Champions League play-off.
Bodo/Glimt and FC Zurich are champions of Norway and Switzerland respectively.