At the draw in Monte Carlo, the revamped 36-team competition threw up a showdown with the Scottish champions and a repeat of Villa’s finest hour, their European Cup victory over Bayern in 1982.
The new format sees all 36 teams forming a single league, with each entrant playing 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.
Manchester City were the first team pulled out by former Italy goalkeeper Gianluigi Buffon.
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.
City’s highlights include clashes with Inter Milan, Juventus and Paris St Germain.
Club Brugge, Feyenoord, Sporting Lisbon, Sparta Prague and Slovan Bratislava are their other five opponents.
Liverpool were the next British team pulled out and landed a home fixture against holders Real Madrid.
Leipzig, Bayer Leverkusen, AC Milan, Lille, PSV Eindhoven, Bologna and Girona made up their schedule.
Arsenal were drawn out of pot two already knowing they would face PSG, Atalanta and Inter Milan.
The rest of their opponents came out as Shakhtar Donetsk, Dinamo Zagreb, Sporting Lisbon, Monaco and Girona.
As well as Villa, Celtic – residing in Pot Three – will face last season’s runners-up Borussia Dortmund, Leipzig, Club Brugge, Atalanta, Young Boys, Dinamo Zagreb and Slovan Bratislava.
Most of the jeopardy had long since passed for Villa, down in Pot Four, who knew all but two of their opponents during a headache-inducing procedure.
Their other seven fixtures will be against Leizpig, Juventus, Club Brugge, Celtic, Young Boys, Bologna and Monaco.
The full fixture list with match dates and kick-off times will be announced on Saturday, August 31.
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