Those two clubs are likely to fight it out for first place in a group that also contains Russian champions CSKA Moscow and Czech club Viktoria Plzen.
The draw was even kinder to 2012 European champions Chelsea. The Blues will face Bundesliga club Schalke, 1986 European Cup winners Steaua Bucharest and FC Basel, who lost to Chelsea in the Europa League semi-finals last season, in Group E.
David Moyes, though, will not be taking the opposition lightly in what will be his first Champions League campaign at the helm of Manchester United.
The English champions will be favourites to qualify for the last 16 from Group A but they must still face Ukraine's Shakhtar Donetsk, Spanish outfit Real Sociedad and Bayer Leverkusen.
The German side beat United in the 2002 semi-finals and are now coached by former Liverpool defender Sami Hyypia.
Arsenal came off the worst of all, the English contenders in a Group F that contains last season's runners-up Borussia Dortmund, Marseille and Napoli.
The Gunners faced Dortmund and Marseille in the group stage two seasons ago, but will be especially wary of Napoli, whose coach Rafael Benitez is a specialist at this level and who, in Gonzalo Higuain, boast a striker that might have joined Arsenal earlier this summer.
Group H is bustling with history, as Barcelona, AC Milan, Ajax and Celtic - with 16 European Cups between them - come together.
This will be third consecutive season in which Barca and Milan have met but, remarkably, the Catalans and Ajax - united by their links to Johan Cruyff - have never faced each other in a competitive game.
Celtic beat Barcelona in last season's competition but their manager Neil Lennon knows the size of task that lies before the Scottish champions.
"I think it's the best and the worst draw we could've got,'' Lennon told Sky Sports News.
"In terms of glamour I don't think it comes any better than Barca, Milan and Ajax, but in terms of football it doesn't come any harder.''
Elsewhere, Real Madrid face Juventus, Galatasaray and FC Copenhagen in Group B.
As a result, new Madrid coach Carlo Ancelotti will come up against the Serie A champions, whom he coached between 1999 and 2001.
Paris Saint-Germain will expect to advance from Group C, which also contains Benfica, Olympiakos of Greece and Belgian champions Anderlecht, while Porto, Atletico Madrid, Zenit St Petersburg and Austria Vienna meet in Group G.
The opening round of group games will be played on September 17 and 18.
-AAP