Holders Saracens and triple European title winners Toulon will meet in the pool stage of next season's Champions Cup.
Saracens, who landed the trophy last month following victory over Racing 92 in Lyon, have been grouped with a club they lost to in the 2014 European final.
The pool is completed by solitary Welsh representatives the Scarlets, while Sale Sharks will ensure two all-Aviva Premiership games against Saracens.
Exeter, beaten by Saracens in last season's Premiership final, are reunited with French heavyweights Clermont Auvergne -- they met twice in the pool stage last term -- while Leicester face recently-crowned French champions Racing 92, who beat them in the Champions Cup semifinals two months ago.
Elsewhere, Wasps are in the same group as four-time European champions Toulouse and Guinness PRO12 title holders Connacht, with Northampton drawn alongside Leinster, Montpellier and Castres.
The European Challenge Cup pool draw, which was also conducted at European Professional Club Rugby headquarters in Neuchatel, Switzerland on Wednesday, produced an intriguing battle of the west country, with Bath and Bristol drawn together.
Bristol, back in European competition following their return to the Aviva Premiership for next season, were grouped alongside Bath, Cardiff Blues and French club Pau.
Harlequins, last season's Challenge Cup runners-up, will meet Edinburgh, Stade Francais and Romanian side Timisoara Saracens in Pool Five, while Gloucester were drawn in Pool One alongside La Rochelle, Treviso and Bayonne.
Elsewhere, Worcester face a long trip to Russia with Enisei-STM in their group, along with Newport Gwent Dragons and Brive, and Newcastle line up in Pool Two alongside Ospreys, Grenoble and Lyon.
Pool One - Racing 92, Glasgow, Leicester, Munster
Pool Two - Connacht, Wasps, Toulouse, Zebre
Pool Three - Saracens, Toulon, Scarlets, Sale Sharks
Pool Four - Leinster, Montpellier, Northampton, Castres
Pool Five - Exeter, Clermont Auvergne, Ulster, Bordeaux-Begles.
Pool One - La Rochelle, Gloucester, Treviso, Bayonne
Pool Two - Ospreys, Grenoble, Newcastle, Lyon
Pool Three - Brive, Worcester, Newport Gwent Dragons, Enisei STM
Pool Four - Cardiff Blues, Bath, Pau, Bristol
Pool Five - Harlequins, Edinburgh, Stade Francais, Timisoara Saracens.