Saracens will begin the defence of their Champions Cup title away at Racing 92, while Challenge Cup champions Clermont Auvergne will face Harlequins.
Premiership holders Saracens became the first English club to win Europe's flagship club tournament for a third time last season, and will get their Pool 4 campaign up and running on November 17.
Reigning Top 14 champions Toulouse get the tournament started two days earlier, taking on Gloucester.
Clermont were hugely impressive as they claimed the Challenge Cup title last term, beating La Rochelle 36-16 in Newcastle, and host Harlequins on November 16.
Benetton, who last season became the first Italian side to qualify by right for Europe's top competition, face PRO14 champions Leinster in their opening fixture.
Meanwhile, the Challenge Cup will kick-off with a clash between Enisei-STM and Worcester Warriors in Krasnodar.
Seven former European title winners – Brive, Cardiff Blues, Leicester Tigers, Pau, RC Toulon, Stade Francais Paris and Wasps – are involved in this season's Challenge Cup, which along with the Champions Cup, will culminate at the Stade Velodrome in May.