Chelsea have been given a relatively kind-looking route to the last 16, while Manchester United will also be quietly optimistic of progressing to the knockout stages.
Celtic have been set the toughest task of the British clubs to qualify for the last 16 after the Scottish champions came out in Group H.
The opponents for Neil Lennon's side are Barcelona, who they faced in last season's group phase, Italian giants AC Milan and Dutch champions Ajax.
City have been given a good chance of reaching the knockout rounds for the first time after landing two high-profile groups in the previous two years.
Though Manuel Pellegrini's side will have to tackle reigning champions Bayern, City will also face Russian outfit CSKA Moscow and Viktoria Plzen from the Czech Republic.
Arsenal, who reached the group phase after a comfortable 5-0 aggregate success over Fenerbahce in the play-offs, have been handed a testing draw in Group F.
In addition to facing Dortmund, Arsenal will also meet French side Marseille and Napoli, who are now coached by former Liverpool and Chelsea boss Rafa Benitez.
Three-times European champions United were drawn in Group A and David Moyes will likely be relatively satisfied with the opponents for his first group campaign as a manager.
United will tackle Ukrainian side Shakhtar Donetsk, Bayer Leverkusen, who beat the Red Devils in the 2002 semi-finals, and Real Sociedad.
Chelsea, with Jose Mourinho now back as manager, have arguably been given the most straightforward group of the British clubs.
Aside from a meeting with 2011 semi-finalists Schalke, Chelsea will also encounter Swiss club Basel and Romanian side Steaua Bucharest.
The Blues knocked out both Basel and Steaua en route to winning last season's Europa League, and also met Schalke in the group phase in 2007/08.
Group B serves up the tantalising prospect of two games between Real Madrid and Juventus, with Galatasaray and FC Copenhagen also in that section.
Last season's Europa League runners-up Benfica were the top seeds in Group C and they will face Paris St Germain, Olympiakos and Anderlecht.
In Group G, 2004 European champions Porto will take on 2010 and 2012 Europa League winners Atletico Madrid, 2008 UEFA Cup winners Zenit St Petersburg and Austria Vienna.
Celtic, who clinched their place in the draw after a dramatic play-off comeback against Shakhter Karagandy, memorably beat Barcelona at Parkhead in last season's group stage last November with a dramatic late goal from Tony Watt.
Milan and Ajax add further glamour to the group, and the four clubs between them have won 16 European titles.
Bhoys boss Lennon told Sky Sports News: "I think it is the best and the worst draw we could have got.
"In terms of glamour I don't think it comes any better than Barcelona, Ajax and AC Milan. In terms of football it is probably the most difficult group we could have got.
"But I think the hard work was really done last night [against Shakhter] and we can go and enjoy the tournament now."
Barcelona star Lionel Messi is looking forward to facing Celtic and Milan again after his side were thrashed by Bayern in the semi-finals last season.
Messi said: "You don't get any easy groups in the Champions League. We played Milan and Celtic last season. It's a beautiful group."
Milan official Umberto Gandini said: "Before the draw, I was close to Barcelona president Rosell. He said that it be Barcelona-Milan again, and so it is.
"It is a well-known group, with prestigious stadia, historical ones, with teams who have already won the Champions League."
Arsenal, who have reached this stage of the competition for 16 successive seasons, also played Dortmund in their group two years ago.
On that occasion Dortmund finished bottom of the section but the Germans are now a much tougher proposition and impressed throughout their run to the final last year.
Napoli's sporting director Riccardo Bigon told Sky Italia: "In this tournament, there are incredible clubs. We are in a really complicated group, but our aim is to overcome this group."
Manchester City director of football Txiki Begiristain insisted after the draw that he was upbeat about his side's chances of advancing from Group D, but admitted CSKA Moscow would be competitive along with favourites Bayern Munich.
He said: "They (CSKA) are the champions of the Russia league and are doing well. They have a good team with some good players and it will be difficult, but we have a lot of confidence this season.
"We have improved the team, we have a new manager with a lot of experience in the Champions League and we hope we will be stronger in the Champions League."
Manchester United secretary John Alexander was also in buoyant mood after David Moyes learned his opponents for his debut campaign in the Champions League group stage.
"It's not a bad draw for your first group stage with Manchester United," said Alexander. "It is very interesting with the German and Spanish sides in there.
"I guess they would be quite tough opposition from pots three and four, and Shakhtar Donetsk is an interesting trip for anybody at any time of the year.
"It's a very exciting group to be in."
As a result of the draw, Sky Bet have pushed Arsenal out from 25/1 to 40/1 to win the Champions League, while Celtic are now 1500/1 from 400/1.
The other three British clubs have seen their odds cut, with Chelsea 9/1 (from 11/1), Manchester City 10/1 (from 12/1) and Manchester United 11/1 (from 12/1).