Mauricio Pochettino's men were paired with holders Real Madrid, German giants Borussia Dortmund and Cypriot underdogs APOEL.
The Londoners will hope to avoid a repeat of last year's disappointing third-placed finish - in a far easier group on paper - as they aim to make Wembley a fortress both domestically and in continental competition.
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Chelsea, meanwhile, will face Atletico Madrid in a delicious twist of fate in the context of the ongoing Diego Costa transfer saga.
The Spaniard is effectively on strike at present as he looks to force through a move back to his former club, who were Champions League runners-up in 2014 and 2016.
Roma will present the Blues with a tricky pair of encounters while the long trip east to face Azerbaijani champions Qarabag is one Antonio Conte and his men are unlikely to relish.
Celtic were drawn alongside Bayern Munich, PSG and Anderlecht after booking their spot in the draw with an 8-4 aggregate triumph over Astana.
The Hoops can count themselves a little unfortunate to have drawn two genuine 'big-hitters' for the second year running, having been paired with Manchester City and Barcelona last term.
However, boss Brendan Rodgers' stated aim is to extend Celtic's European involvement into 2018 and a potential battle with Anderlecht for third place and Europa League qualification presents that opportunity.
United drew Benfica - who they famously beat in the 1968 European Cup final - Basel and CSKA Moscow.
All three have plenty of Champions League experience but they are unlikely to strike fear into the hearts of Jose Mourinho's early Premier League pace-setters.
Similarly, Liverpool look to have a superb chance of advancing after securing their group-stage place for just the second time in eight years with Wednesday's 4-2 win over Hoffenheim at Anfield.
The Reds were paired with Spartak Moscow, Sevilla - who beat them in the 2016 Europa League final - and NK Maribor.
City, meanwhile, will tackle Shakhtar Donetsk, Napoli and Feyenoord.
All three away assignments are potentially problematic on paper - the Italians in particular boast a proud record at their raucous San Paolo home - but Pep Guardiola will expect to steer his charges into the last 16.
Elsewhere, Barcelona will face last year's runners-up Juventus, who beat the Spanish giants 3-0 on aggregate in the semi-finals before eventually succumbing to Real Madrid in Cardiff.
FULL CHAMPIONS LEAGUE 2017/18 GROUP-STAGE DRAW:
Group A: Benfica, MANCHESTER UNITED, Basel, CSKA Moscow
Group B: Bayern Munich, PSG, Anderlecht, CELTIC
Group C: CHELSEA, Atletico Madrid, Roma, Qarabag
Group D: Juventus, Barcelona, Olympiakos, Sporting CP
Group E: Spartak Moscow, Sevilla, LIVERPOOL, NK Maribor
Group F: Shakhtar Donetsk, MANCHESTER CITY, Napoli, Feyenoord
Group G: Monaco, Porto, Besiktas, RB Leipzig
Group H: Real Madrid, Borussia Dortmund, TOTTENHAM HOTSPUR, APOEL
When will the matches be played?
The games will be played on Tuesdays and Wednesdays across six matchdays, which take place on the following dates:
Matchday 1: September 12th/13th
Matchday 2: September 16th/17th
Matchday 3: October 17th/18th
Matchday 4: October 31st/November 1st
Matchday 5: November 21st/22nd
Matchday 6: December 5th/6th