Barcelona, Dortmund and Inter, with nine European Cups between them, were drawn together in Group F along with the Czech champions Slavia Prague.
Beaten by Liverpool in the semi-finals last season, Lionel Messi and Barcelona remain favourites to advance as they seek a first Champions League crown since 2015.
Dortmund won the trophy in 1997 and lost in the final in 2013. Now coached by Antonio Conte, Inter beat Barcelona in the semi-finals en route to winning the most recent of their three titles in 2010.
"That really is a very tough group, which makes it an even bigger challenge for us," said the Dortmund coach, Lucien Favre.
Liverpool advanced from their group at the expense of Napoli last season on the way to lifting their sixth European Cup in Madrid, and Carlo Ancelotti's side now have a chance to gain revenge.
Both clubs will be fancied to progress from Group E, which is completed by Austrian champions Salzburg and Genk, the Belgian title-holders.
"Napoli again! I don't know how often I've now played against Napoli, but they're obviously a very experienced side," said Liverpool boss Jurgen Klopp, who faced the Italians with Dortmund in the 2013-14 group stage.
Liverpool are hoping to return to this year's final which will be played in Istanbul, where they won their fifth title back in 2005.
After losing in last season's final, Tottenham Hotspur can look forward to a meeting with German champions Bayern Munich in Group B.
That will be the first meeting of the clubs since the 1983-84 UEFA Cup. They will also meet Greek champions Olympiakos and Red Star Belgrade of Serbia, the 1991 European Cup winners, in Group B.
After winning the Europa League, Chelsea are back in the Champions League and can look forward to taking on last season's semi-finalists Ajax as well as former Champions League runners-up Valencia and Lille in Group H.
Premier League champions Manchester City were handed the kindest draw of all four English representatives, with Pep Guardiola's men coming up against Italian debutants Atalanta along with Shakhtar Donetsk and Dinamo Zagreb in Group C.
City beat Shakhtar 3-0 in Ukraine in last season's group stage before a 6-0 victory in the return fixture.
"We have to keep being strong in our country and if we do that, we know we will have a chance in this competition," said Txiki Begiristain, the director of football at City, who have lost in the quarter-finals in each of the last two seasons.
There will be glamour ties between familiar opponents elsewhere, with Zinedine Zidane's Real Madrid renewing acquaintances with Paris Saint-Germain in Group A.
Real eliminated the French champions in the last 16 on the way to winning the trophy two seasons ago.
Turkish champions Galatasaray and Club Brugge of Belgium complete Group A.
Cristiano Ronaldo and Juventus will come up against Atletico Madrid again after beating the Spanish side in the last 16 last season. They will also face Bayer Leverkusen and Lokomotiv Moscow in Group D.
"I don't know what's going to happen this year but when the year starts I'm always confident. This year I'm not changing my mind," Ronaldo, whose side lost to Ajax in the quarter-finals last season, told BT Sport.
Perhaps the most balanced section sees Zenit Saint Petersburg, Benfica, Lyon and RB Leipzig clash in Group G. The first fixtures in all groups will be played on September 17 and 18.
Draw for the 2019/20 Champions League group stage, made in Monaco on Thursday:
Paris Saint-Germain (FRA), Real Madrid (ESP), Club Brugge (BEL), Galatasaray (TUR)
Bayern Munich (GER), Tottenham (ENG), Olympiakos (GRE), Red Star Belgrade (SRB)
Manchester City (ENG), Shakhtar Donetsk (UKR), Dinamo Zagreb (CRO), Atalanta (ITA)
Juventus (ITA), Atletico Madrid (ESP), Bayer Leverkusen (GER), Lokomotiv Moscow (RUS)
Liverpool (ENG), Napoli (ITA), Red Bull Salzburg (AUT), Genk (BEL)
Barcelona (ESP), Borussia Dortmund (GER), Inter Milan (ITA), Slavia Prague (CZE)
Zenit Saint-Petersburg (RUS), Benfica (POR), Lyon (FRA), RB Leipzig (GER)
Chelsea (ENG), Ajax (NED), Valencia (ESP), Lille (FRA)
The confirmed first round of fixtures in this season's UEFA Champions League following Thursday's draw in Monaco (all kick-offs 21:00 SA time unless stated):
Tuesday, September 17
At Naples, Italy
Napoli (ITA) v Liverpool (ENG)
At Salzburg, Austria
Salzburg (AUT) v Genk (BEL)
At Milan, Italy (18:55)
Inter Milan (ITA) v Slavia Prague (CZE)
At Dortmund, Germany
Borussia Dortmund (GER) v Barcelona (ESP)
At Lyon, France (18:55)
Lyon (FRA) v Zenit Saint Petersburg (RUS)
Benfica (POR) v RB Leipzig (GER)
Chelsea (ENG) v Valencia (ESP)
Ajax (NED) v Lille (FRA)
Wednesday, September 18
At Bruges, Belgium (18:55)
Club Brugge (BEL) v Galatasaray (TUR)
Paris Saint-Germain (FRA) v Real Madrid (ESP)
At Piraeus, Greece (18:55)
Olympiakos (GRE) v Tottenham Hotspur (ENG)
Bayern Munich (GER) v Red Star Belgrade (SRB)
At Kharkiv, Ukraine
Shakhtar Donetsk (UKR) v Manchester City (ENG)
Dinamo Zagreb (CRO) v Atalanta (ITA)
Atletico Madrid (ESP) v Juventus (ITA)
At Leverkusen, Germany
Bayer Leverkusen (GER) v Lokomotiv Moscow (RUS)
Matchday 2: October 1/2
Matchday 3: October 22/23
Matchday 4: November 5/6
Matchday 5: November 26/27
Matchday 6: December 10/11