The final will be played at Cardiff's Millennium Stadium on May 24 or 25 next year.
Bristol's reward for an outstanding third-place finish in the Guinness Premiership last season is to be drawn against French champions Stade Francais, Cardiff and Harlequins.
Magners League champions the Ospreys are the top seeds in pool two, which also features beaten Premiership finalists Gloucester, Bourgoin and Ulster.
Newport Gwent Dragons won a play-off to claim the last available place in the European Cup and draw pool one seeds Treviso, London Irish and Perpignan.
Biarritz would be favourites to win pool four, which also includes Saracens and Viadana, despite Glasgow being the top seeds.
European Rugby Cup selects seeds for each group by country rather than on merit, which leads to a lop-sided draw. And Wasps will be hugely frustrated.
The last time they were defending champions, in 2005, Wasps were drawn against Leicester and Biarritz.
This time around, the task of qualifying for the knock-out stages is even harder. The six group winners and two best-placed runners-up reach the quarter-finals.
But Wasps face a Llanelli side who reached last year's semi-finals, 2006 European champions Munster and Clermont Auvergne, who reached the French championship final last Saturday.
All four of those teams would enter the tournament with genuine aspirations of winning the title in Cardiff next May.
Almost the same situation occurs in pool six, where three-times champions Toulouse and two-time winners Leicester are in with last year's quarter-finalists Leinster.
The first round of matches take place on the weekend of November 9-11.