The 20-team tournament will replace the European Challenge Cup as Europe's second-tier competition for rugby clubs and there are five RaboDirect PRO12 entries in all.
The Blues, who beat Toulon 28-21 in the 2010 showpiece, line up alongside London Irish, Grenoble and an undetermined club which will be decided from a qualifying competition.
In Pool 2 Connacht - three-time semi-finalists in the Challenge Cup - will face off with Exeter Chiefs, Bayonne and La Rochelle.
Pool 3 comprises of Newport Gwent Dragons, Stade Francais, Newcastle and a second undetermined team.
Edinburgh, who finished eighth in the 2013/2014 RaboDirect PRO12 table, were drawn with Bordeaux Begles, London Welsh and Lyon in Pool 4 while Zebre are in Pool 5 alongside Gloucester, Brive and Oyonnax.
Pool 1: Cardiff Blues, London Irish, Grenoble, FIRA 1
Pool 2: Connacht, Exeter Chiefs, Bayonne, La Rochelle
Pool 3: Newport Gwent Dragons, Stade Francais, Newcastle, FIRA 2
Pool 4: Edinburgh, Bordeaux Begles, London Welsh, Lyon
Pool 5: Zebre, Gloucester, Brive, Oyonnax
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