Champions League debutants Manchester City have been drawn against German side Bayern Munich, Spanish outfit Villarreal and Italian club Napoli.
Last season's finalists Manchester United will compete in Group C along with Benfica, Basel and Otelul Galati.
Arsenal, who qualified via victory over Udinese, will face Marseille, Olympiakos and Borussia Dortmund.
Chelsea were assigned to Group E with Valencia, Bayer Leverkusen and Genk in Thursday's draw in Monaco.
Spanish four-time winners and current holders Barcelona are in Group H along with seven-time European champions AC Milan from Italy, Belarusian side BATE Borisov - making their second appearance in the competition - and group stage debutants Viktoria Plzen from the Czech Republic.
Barca's domestic rivals Real Madrid, who have won the tournament a record nine times, face competition from French side Lyon, Dutch champions Ajax and Dinamo Zagreb from Croatia.
Italian side Inter Milan, who won the competition in 2010, have been presented with a relatively straight-forward group containing Russian club CSKA Moscow, French outfit Lille and Turkish team Trabzonspor, who were entered into the tournament on Wednesday after Fenerbahce were withdrawn in the wake of an ongoing investigation into match fixing.
Group G contains Portuguese side Porto, Shakhtar Donetsk from Ukraine, Russian club Zenit St Petersburg and APOEL Nicosia of Cyprus.
Of all the English sides, City's draw appears to be the toughest.
Although Bayern Munich and Villarreal both had to come through play-offs to qualify for the group stages, each has a wealth of Champions League experience and talented players at their disposal.
Napoli finished third in Serie A last season and have been able to hold on to the core of the team that got them there.
However football administration officer Brian Marwood said that there was excitement at the club from simply being involved.
"It's a fantastic group. It's going to be extremely competitive and I genuinely believe there are four teams that can compete for the two spots on an even keel," he said.
"This is a fantastic part of Manchester City's history to be part of the competition and our fans will enjoy every minute of this year's Champions League tournament.
"We have a squad now that is blessed with great talent, spirit and endeavour and we feel we are more than capable of competing with the best in this tournament.
"This is new to us as a club but we have players with Champions League experience and they know what playing in this tournament is all about."
United's group appears the easiest on paper, and though Arsenal have to play German champions Borussia Dortmund, they should be confident of overcoming both Marseille and Olympiakos.
"We've had great success in the competition over the years and we are looking forward to it immensely," said United chief executive David Gill.
"I got a text from Sir Alex and he is happy, we have a new Romanian team, congratulations to them and we look forward to going there. They are the new boys and we are happy to get that draw. We are comfortable with the draw we've been given.
"We have a young team and a vibrant squad and we feel we are well equipped for the months ahead."
Chelsea too should view themselves as more than capable of progressing to the knockout stages in Andre Villas-Boas' first season in charge.
Champions League group stage draw in full:
Bayern Munich, Villarreal, Manchester City, Napoli
Inter Milan, CSKA Moscow, Lille, Trabzonspor
Manchester United, Benfica, Basel, Otelul Galati
Real Madrid, Lyon, Ajax, Dinamo Zagreb
Chelsea, Valencia, Bayer Leverkusen, Genk
Arsenal, Marseille, Olympiakos, Borussia Dortmund
Porto, Shakhtar Donetsk, Zenit St Petersburg, APOEL Nicosia
Barcelona, AC Milan, BATE Borisov, Viktoria Plzen