Exeter will face European Champions Toulon in the Heineken Cup next season.
The Chiefs have been drawn with the French giants in Pool 2 while Premiership champions Leicester Tigers will have good chances to qualify for the quarter-finals facing Pro12 finalists Ulster, Montpellier and Treviso.
Northampton Saints will face a tough group in Pool with clashes with Irish giants Leinster, Top 14 champions Castres and the Ospreys.
Harlequins have also a huge task ahead in Pool 4 with French duo Clermont and Racing Metro and the Scarlets.
In the Amlin Challenge Cup, Sale and Worcester have been drawn in the same group with Biarritz and French ProD2 Champions Oyonnax.
Championship champions Newcastle Falcons will face Brive who have also been promoted after only one season in the French tier-two.
Heineken Cup – Pool Draw:
Pool 1 – Leinster, Northampton Saints, Ospreys, Castres
Pool 2 – Toulon, Cardiff Blues, Glasgow, Exeter Chiefs
Pool 3 – Toulouse, Saracens, Connacht, Zebre
Pool 4 – Clermont Auvergne, Harlequins, Scarlets, Racing Metro
Pool 5 – Ulster, Leicester, Montpellier, Treviso
Pool 6 – Munster, Perpignan, Edinburgh, Gloucester
Amlin Challenge Cup – Pool Draw:
Pool 1 – Biarritz Olympique PB, Sale Sharks, Worcester Warriors, Oyonnax
Pool 2 – Bath Rugby, Newport Gwent Dragons, Bordeaux-Bègles, Mogliano Rugby
Pool 3 – Brive, Newcastle Falcons, Cammi Rugby Calvisano, Bucharest Wolves
Pool 4 – London Wasps, Rugby Viadana, Bayonne, Grenoble
Pool 5 – Stade Français Paris, London Irish, I Cavalieri Prato, Olympus Rugby XV