Clubs were divided into two pools of 12 – Pool A and Pool B – by means of a draw in Dublin.
All 24 teams play two sides home and away across four rounds of pool fixtures in December and January.
The top eight teams in each pool of 12 progress to a round of 16, followed by quarter-finals and semi-finals, with Dublin’s Aviva Stadium hosting the final next May.
Three English clubs will face trips to South Africa in the pool stage.
South African sides the Stormers, Bulls and Sharks qualified from the United Rugby Championship to make their tournament bow.
London Irish will visit newly crowned URC champions the Cape Town-based Stormers, while Exeter meet the Bulls in Pretoria and Harlequins travel to Durban for an appointment with the Sharks.
Irish also meet French champions Montpellier, with Exeter tackling Castres and Quins facing Racing 92.
Elsewhere, Premiership champions Leicester encounter Clermont Auvergne – Tigers beat them home and away this season – and Ospreys, while Saracens take on Lyon and Edinburgh.
Northampton face Champions Cup holders La Rochelle, plus Munster, while Gloucester meet Leinster and Bordeaux-Begles, with Sale tackling Toulouse and Dan McFarland's Ulster side.
In the second-tier European Challenge Cup, Worcester will travel to South Africa to face the Johannesburg-based Lions.
South Africa’s second Challenge Cup team, the Cheetahs, are set to play their home games in Europe, with Scarlets one of their opponents.
Bath have arguably the toughest draw of England’s five representatives, facing Toulon and Glasgow.
Champions Cup Pool A: Castres, Saracens, Bulls, Lyon, Exeter, Edinburgh, Bordeaux-Begles, Harlequins, Leinster, Racing 92, Gloucester, Sharks.
Pool B: Montpellier, Leicester, Stormers, Clermont Auvergne, London Irish, Ospreys, Toulouse, Northampton, Ulster, La Rochelle, Sale, Munster.
Challenge Cup Pool A: Glasgow, Toulon, Bristol, Zebre Parma, Perpignan, Bath, Connacht, Cardiff, Brive, Newcastle.
Pool B: Scarlets, Pau, Wasps, Dragons RFC, Bayonne, Cheetahs, Lions, Benetton, Stade Francais, Worcester.