Chelsea boss Jose Mourinho will return to his former club Porto for the group stage of the Champions League.
Mourinho won the Champions League as Porto coach last season
Chelsea will also face Paris St Germain and CSKA Moscow, while Arsenal have been drawn with Panathanaikos, PSV Eindhoven and Rosenborg.
Manchester United meet Lyon, Sparta Prague and Fenerbahce.
Liverpool will play Deportivo, Monaco and Olympiakos, while Celtic's group includes AC Milan, Barcelona and Shakhtar Donetsk.
The Scottish champions are set to meet up with their former star striker Henrik Larsson, who moved to Barcelona on a free in the summer.
Mourinho led Porto to a surprise Champions League win last season and Chelsea chief executive Peter Kenyon said they were looking forward to the games.
"That's the way it works," said Kenyon. "I guess that was always one of the predictable ones.
"But we shouldn't forget the other teams. There are no easy games but we've got some great experience from Jose who has won the competition.
"You have to be happy with our group and I think we're in for some interesting football."
Liverpool chief executive Rick Parry feels only time will tell whether his side's draw proves favourable or not.
He said: "Rafael Benitez will know all about Deportivo, Monaco didn't do badly last year and we've been to Olympiakos before.
14 Sept: Arsenal v PSV
14 Sept: Celtic v Barca
14 Sept: PSG v Chelsea
15 Sept: Liverpool v Monaco
15 Sept: Lyon v Man Utd
"We've avoided the very biggest but that doesn't mean we've avoided the best - last year it was some of the smaller teams that did very well.
"We will treat them all with respect but not with fear."
Manchester United's draw will have pleased Sir Alex Ferguson according to the club's chief executive David Gill.
"It's going to be an exciting group and we're looking forward to it," Gill said. "We will have to ask Alex but I'm sure he'll be extremely happy."
Arsenal director Danny Fiszman said he was also satisfied with the group his side had been given.
Fiszman said: "We've managed to stay away from the Italian sides and we're happy about that."
Champions League group draw:
Deportivo La Coruna (Spain)
Real Madrid (Spain)
AS Roma (Italy)
Bayer Leverkusen (Germany)
Dynamo Kiev (Ukraine)
Bayern Munich (Germany)
Ajax Amsterdam (Holland)
Maccabi Tel Aviv (Israel)
Manchester United (England)
Olympique Lyon (France)
Sparta Prague (Czech Republic)
PSV Eindhoven (Holland)
Rosenborg Trondheim (Norway)
AC Milan (Italy)
Shakhtar Donetsk (Ukraine)
Inter Milan (Italy)
Werder Bremen (Germany)
Paris St Germain (France)
CSKA Moscow (Russia)
Opening matches 14/15 September.