Premier League champions City, in the second pot of seeds, face Bayern and CSKA Moscow again, with Roma making up a tough Group E.
Arsenal, who qualified after beating Besiktas in the play-offs, were among the top seeds but got Dortmund for a second successive campaign. Group D also contains Galatasaray and Anderlecht.
Liverpool have to contend with defending champions Real Madrid, but - despite the Reds being in the third pot of seeds - they will be pleased that FC Basel and Bulgarian heroes Ludogorets are the other two sides.
Chelsea got one of the easiest groups, with Schalke, Sporting Lisbon and Celtic-conquering Maribor their oppponents.
Group F pits Barcelona and Paris Saint-Germain again, with Ajax - like Barca an ex-club of PSG striker Zlatan Ibrahimovic - also involved; despite being in the bottom pool of seeds, Monaco got a decent draw of Benfica, Zenit St Petersburg and Bayer Leverkusen.
Russian and Ukrainian clubs were kept apart in the draw due to the ongoing conflict in the east of Ukraine. One of the teams based in the conflict zone, Shakhtar Donetsk, will face FC Porto, Athletic Bilbao and BATE Borisov.
Champions League Draw
FULL GROUP DRAW
A: Atletico Madrid, Juventus, Olympiacos, Malmo
B: Real Madrid, FC Basel, Liverpool, Ludogorets
C: Benfica, Zenit St Petersburg, Bayer Leverkusen, Monaco
D: Arsenal, Borussia Dortmund, Galatasaray, Anderlecht
F: Barcelona, Paris St-Germain, Ajax, APOEL
G: Chelsea, Schalke, Sporting Lisbon, Maribor
H: FC Porto, Shakhtar Donetsk, Athletic Bilbao, BATE Borisov
WHAT THEY SAID
Bayern sports director Matthias Sammer: "The group is hugely attractive but also very, very difficult. It is, however, also the right challenge for us."
Manchester City's director of football Txiki Begiristain: "It's a very, very, tough group. They are very strong teams. I think (it's the toughest group). It's spectacular all the clubs try to play good football. It will be an amazing group. We are happy with the squad we have for this season. We've signed some very good players. We want to improve in the Champions League."
Barcelona sporting director Andoni Zubizarreta: "When you start your draw with PSG, you know that they have a very difficult opponent. After that, we have Ajax which is a team historically very closely linked to Barca. We had never played against them in Europe and this is the second season running that happens, history repeats itself. Apoel is a novelty for us but my memory tells me that Apoel in Europe is always a very difficult team to beat. We will play in the same way against PSG as against Ajax or any other team."
Ajax director Edwin van der Sar: See video
Borussia Dortmund sports director Michael Zorc: "This looks to me like an evenly balanced group and we should expect a lot of suspense. As for Champions League duels with Arsenal, there we have our share of experience. Borussia Dortmund go into the group stage that is no doubt difficult with a lot of confidence."
The happiest man there seemed to be Ludogorets coach Georgi Dermendzhiev. His minnows were on the brink of losing their play-off against Steaua Bucharest before scoring a last-minute equaliser. They went on to win the penalty shoot out with a defender in goal after their keeper was sent off - that defender, Cosmin Moti, scored a penalty and saved two to send his team through for the first time.
"I'm happy with the draw," Dermendzhiev said. "Real Madrid will blow up Bulgaria and so many people will be able to see them thanks to Ludogorets. Liverpool are a very strong team too and we know Basel because we met them last year. We'll win some points, I just don't want to play against Real in the first match. I can assure you that you'll see a stronger Ludogorets from now on."
- Sports & Recreation
- Real Madrid
- Borussia Dortmund
- Manchester City
- FC Basel
- Premier League
- Bayer Leverkusen
- Paris Saint-Germain
- Atletico Madrid
- Bayern Munich
- Shakhtar Donetsk
- Zenit St Petersburg
- Sporting Lisbon