The draw was attended by a host of soccer legends and current stars, including Eusebio, Bobby Charlton, Zinedine Zidane, and Cristiano Ronaldo.
Zenit, the current UEFA Cup holders, are making their debut in Europe's most prestigious club competition, while BATE are the first Belarusian side to appear in the Champions League group stages.
The first round of matches will be played on 16/17 September.
The Russian champions face Manchester United in the Super Cup in Monaco on Friday, the annual money-spinner between the Champions League and UEFA Cup holders. Manchester United were drawn in Group E with Scottish champions Celtic, Spain's Villarreal, and Danish side Aalborg.
In other Russian soccer news, FC Moskva defeated Legiya Warsaw 2-0 in Moscow, 3-0 on aggregate, on Wednesday to make the first round of the UEFA Cup.
2008/09 UEFA Champions League group stage
Group A
Chelsea FC (ENG)
AS Roma (ITA)
FC Girondins de Bordeaux (FRA)
CFR 1907 Cluj (ROM)
Group B
FC Internazionale Milano (ITA)
Werder Bremen (GER)
Panathinaikos FC (GRE)
Anorthosis Famagusta FC (CYP)
Group C
FC Barcelona (SPA)
Sporting Clube de Portugal (POR)
FC Basel 1893 (SUI)
FC Shakhtar Donetsk (UKR)
Group D
Liverpool FC (ENG)
PSV Eindhoven (NED)
Olympique de Marseille (FRA)
Club Atletico de Madrid (SPA)
Group E
Manchester United FC (ENG, holders)
Villarreal CF (SPA)
Celtic FC (SCO)
Aalborg BK (DEN)
Group F
Olympique Lyonnais (FRA)
FC Bayern Munchen (GER)
FC Steaua Bucuresti (ROM)
ACF Fiorentina (ITA)
Group G
Arsenal FC (ENG)
FC Porto (POR)
Fenerbahce SK (TUR)
FC Dynamo Kyiv (UKR)
Group H
Real Madrid CF (SPA)
Juventus (ITA)
FC Zenit St. Petersburg (RUS)
FC BATE Borisov (BLR)
