Celtic face a huge task to qualify for the Champions League knockout stages after being drawn in the same group as Barcelona, AC Milan and Ajax.
Manchester City take on holders Bayern Munich, CSKA Moscow and Viktoria Plzen.
Arsenal have a tricky start versus Borussia Dortmund, Marseille and Napoli while new Manchester United boss David Moyes is up against Shakhtar Donetsk, Bayer Leverkusen and Real Sociedad.
Chelsea have an easier group of Schalke, FC Basel and Steaua Bucharest.
The first round of group matches will be played on 17-18 September.
Celtic scraped through to the group stage with a dramatic play-off win over Shakhter Karagandy but now face three teams with 15 European Cups between them.
Although the 1967 European Cup winners were drawn last in their group because of their seeding, they did beat Barcelona at Celtic Park in last season's group stage.
Manager Neil Lennon said: "I think it's the best and the worst draw we could have got. In terms of glamour it doesn't come any better than Barcelona, AC Milan and Ajax but in terms of football it doesn't come any harder.
"I think the hard work was done [against Shakhter Karagandy], so now we can enjoy it."
Manchester City, who have not qualified for the group stages for the past two years after being handed tough groups, will relish the chance to progress under new boss Manuel Pellegrini, who took Malaga to the quarter-finals last season.
City lost 2-0 to Bayern in the group stages two years ago in Munich, but beat them by the same scoreline once the German side had qualified.
City captain Vincent Kompany tweeted: "Interesting draw. Big year for us."
Manchester City's director of football Txiki Begiristain said: "We have to do better in the Champions League.
"There's no minimum target. We are big club, with big players and with a manager with big experience.
"We are very, very happy with our squad. We have a minimum of two very good players in each position so it's deep enough."
Arsenal, the only one of the eight top-seeded teams not to have won the competition, qualified for the last 32 after beating Fenerbahce 5-0 in a two-legged play-off.
But of the four English teams in the competition, they appear to have the biggest challenge against last season's runners-up Borussia Dortmund, French Ligue 1 runners-up Marseille and Rafael Benitez's Napoli, who qualified for the last 16 ahead of Manchester City two years ago.
Dortmund coach Jurgen Klopp, whose side failed to beat the Gunners in either of their 2011 meetings, said: "It's a fantastic, even group. It includes four teams who are all capable of going through.
"The fact is, we've got a bit of a score to settle with Arsenal and we also have some revenge to get on Marseille."
Chelsea boss Jose Mourinho will be attempting to win the Champions League with a third different club and his side will be expected to reach the knockout stages, having failed to do so last year.
Moyes, too, has a negotiable group as he manages a team at this stage for the first time. His only previous Champions League experience is with Everton, who were beaten in the qualifying round by Villarreal in 2005.
The 2014 Champions League final will be held at Benfica's Stadium of Light in Lisbon.
Full Champions League draw:
Group A: Manchester United, Shakhtar Donetsk, Bayer Leverkusen, Real Sociedad
Group B: Real Madrid, Juventus, Galatasaray, FC Copenhagen
Group C: Benfica, Paris St-Germain, Olympiakos, Anderlecht
Group D: Bayern Munich, CSKA Moscow, Manchester City, Viktoria Plzen
Group E: Chelsea, Schalke, FC Basel, Steaua Bucharest
Group F: Arsenal, Marseille, Borussia Dortmund, Napoli
Group G: Porto, Atletico Madrid, Zenit St Petersburg, Austria Vienna
Group H: Barcelona, AC Milan, Ajax, Celtic