Brendan Rogers' side face the club managed by Guus Hiddink and captained by Samuel Eto'o in Group A.
Udinese, third in Serie A last season, and the Swiss club complete the group.
Tottenham, like Liverpool, were amongst the top seeds and Andre Villas Boas' outfit will face another Italian team in Lazio in Group J.
Lazio bought former England international Paul Gascoigne from Tottenham in 1992 for £5.5 million pounds and general manager Maurizio Manzini said he planned to invite the ex-player to Rome for the match against Spurs.
"Tottenham is a team Lazio knows very well, a great team with great traditions and we are very familiar with White Hart Lane starting from the time we had Paul Gascoigne.
"There is always a corner of Tottenham in our hearts. He is a mythical figure for Lazio fans and very popular in general in Italy.
"I hope we will have the chance to see him in London and for sure we will invite him to the match in Rome."
Greeks Panathinaikos and Maribor of Slovenia are also in their pool.
And Newcastle United face Bordeaux, Club Brugge and Maritimo in Group D.
Europa League winners Atletico Madrid will face Hapoel Tel Aviv, Viktoria Plzen and newcomers Academica Coimbra from neighbouring Portugal in the group stage of this season's competition.
"We have never played any of these teams. We could have had tougher rivals but we have these, and we will fight to be champions of the group," Atletico president Enrique Cerezo said.
Athletic Bilbao, beaten by Atletico in last season's final face Olympique Lyon, Sparta Prague and Hapoel Kiryat Shmona in another of the 12 groups that comprise the opening stage of UEFA's secondary European club competition.
This season's competition, which begins on September 20 and ends with the final in Amsterdam on May 15 next year has five former European champions, including Olympique Marseille, who face tough opposition from Fenerbache of Turkey, Borussia Moenchengladbach of Germany as well as AEL Limassol of Cyprus.
Marseille coach Elie Baup said: "This is a high-quality draw. We expect hot and high intensity games.
"Fenerbahce and Moenchengladbach have their place in the top European circle. These opponents fully know what the European ties demand. Even if it's not the Champions League, this is a high level European competition."
Inter Milan, European champions in 2010, also face a tough looking group against the hard-to-beat Russians Rubin Kazan, Partizan Belgrade and debutants Nefti from Azerbaijan.
Olympique Lyon, while never winning the Champions League, had qualified for that competition for 13 successive seasons and club president Jean-Michel Aulas said: "Of course we would rather be in the other competition but it would be a major honour to win this title and that is what we are going to try and do."
The top two in each of the 12 groups will join the eight third-placed teams from the Champions League groups in the last 32 of the competition.
Group A: Liverpool (ENG), Udinese (ITA), Young Boys (SUI), Anzhi (RUS)
Group B: Atletico Madrid (SPN), Hapoel Tel-Aviv (ISR), Viktoria Plzen (CZE), Academica (POR)
Group C: Marseille (FRA), Fenerbahce (TUR), Borussia Monchengladbach (GER), AEL Limassol (CYP)
Group D: Bordeaux (FRA), Club Brugge (BEL), Newcastle United (ENG), Maritimo (POR)
Group E: Stuttgart (GER), FC Copenhagen (DEN), Steaua Bucharest (ROU), Molde (NOR)
Group F: PSV Eindhoven (NED), Napoli (ITA), Dnipro (UKR), AIK Solna (SWE)
Group G: Sporting Lisbon (POR), FC Basel (SUI), Genk (BEL), Videoton (HUN)
Group H: Internazionale (ITA), Rubin Kazan (RUS), Partizan Belgrade (SRB), Neftci (AZE)
Group I: Lyon (FRA), Athletic Bilbao (SPN), Sparta Prague (CZE), Hapoel Kiryat Shmona (ISR)
Group J: Tottenham Hotspur (ENG), Panathinaikos (GRE), Lazio (ITA), Maribor (SVN)
Group K: Bayer Leverkusen (GER), Metalist Kharkiv (UKR), Rosenborg (NOR), Rapid Vienna (AUT)
Group L: Twente (NED), Hannover (GER), Levante (SPN), Helsingborg (SWE)
- Paul Gascoigne
- Atletico Madrid