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Liverpool will face Champions League holders Real Madrid on their return to the competition following the draw for the new-look format.
Manchester City and Arsenal both play Paris St-Germain in their fixtures, while Aston Villa take on Scottish champions Celtic.
Each team plays eight fixtures in the 'league phase', with this year's men's tournament seeing a radical change, including the end of a group stage.
The high-tech draw took place in Monaco on Thursday, with Portugal forward Cristiano Ronaldo pressing the all-important button to make a computer algorithm determine the fixtures.
A Uefa video shown before the draw used stars from across the game showing their confusion at the new format, before former Swedish star Zlatan Ibrahimovic praised it for "more football" in a comical interaction with Uefa president Aleksander Ceferin.
The order of matches will be confirmed on Saturday, after the Europa League and Conference League draws have been made.
Aston Villa
Bayern Munich (H)
Leipzig (A)
Juventus (H)
Club Bruges (A)
Celtic (H)
Young Boys (A)
Bologna (H)
Monaco (A)
Arsenal
Paris St-Germain (H)
Inter Milan (A)
Shakhtar Donetsk (H)
Atalanta (A)
Dinamo Zagreb (H)
Sporting Lisbon (A)
Monaco (H)
Girona (A)
Celtic
Aston Villa (A)
Leipzig (H)
Borussia Dortmund (A)
Club Bruges (H)
Atalanta (A)
Young Boys (H)
Dinamo Zagreb (A)
Slovan Bratislava (H)
Liverpool
Real Madrid (H)
Leipzig (A)
Leverkusen (H)
AC Milan (A)
Lille (H)
PSV Eindhoven (A)
Bologna (H)
Girona (A)
Manchester City
Inter Milan (H)
Paris St-Germain (A)
Club Brugge (H)
Juventus (A)
Feyenoord (H)
Sporting Lisbon (A)
Sparta Prague (H)
Slovan Bratislava (A)