Arsenal will face Inter Milan, Paris Saint-Germain and Atalanta among their eight opening fixtures in the first stage of the new-look Champions League.
The revamped format sees all 36 teams forming a single league, with each entrant four home games and four away.
The top eight will go straight into the last 16 while a round of play-offs will decide the other eight teams.
The exact fixtures schedule will be confirmed by Uefa on Saturday.
The Gunners, in Pot 2, will be relatively happy with their Pot 1 opponents. The rest of their opponents came out as Shakhtar Donetsk, Dinamo Zagreb, Sporting Lisbon, Monaco and Girona.
Manchester City will face Inter, Juventus and PSG in a slightly tougher draw on paper, along with Club Brugge, Feyenoord, Sporting Lisbon, Sparta Prague and Slovan Bratislava.
Liverpool were the next British team pulled out by former Italy goalkeeper Gianluigi Buffon at the draw in Monte Carlo.
Cristiano Ronaldo was the man then tasked with pushing a large button on the desk in front of him to allocate eight computer-generated opponents.
The Reds were given fixtures against holders Real Madrid, Leipzig, Bayer Leverkusen, AC Milan, Lille, PSV Eindhoven, Bologna and Girona.
Scottish champions Celtic, residing in Pot 3, were handed an all-British tie at Aston Villa.
They will also face last season's runners-up Borussia Dortmund, Leipzig, Club Bruges, Atalanta, Young Boys, Dinamo Zagreb and Slovan Bratislava.
Aston Villa, back at Europe’s top table after 41 years, will face Bayern, Leipzig, Juventus, Club Brugge, Celtic, Young Boys, Bologna and Monaco.
Champions League draw in full for British teams
Manchester City: Inter Milan (H), PSG (A), Club Brugge (H), Juventus (A), Feyenoord (H), Sporting (A), Sparta Prague (H), Slovan Bratislava (A)
Liverpool: Real Madrid (H), RB Leipzig (A), Bayer Leverkusen (H), AC Milan (A), Lille (H), PSV (A), Bologna (H), Girona (A)
Arsenal: PSG (H), Inter Mian (A), Shakhtar Donestk (H), Atalanta (A), Dinamo Zagreb (H), Sporting (A), Monaco (H), Girona (A)
Celtic: RB Leipzig (H), Borussia Dortmund (A), Club Brugge (H), Atalanta (A), Young Boys (H), Dinamo Zagreb (A), Slovan Bratislava (H), Aston Villa (A)
Aston Villa: Bayern Munich (H), RB Leipzig (A), Juventus (H), Club Brugge (A), Celtic (H), Young Boys (A), Bologna (H), Monaco (A)
