Northampton, who lost out to Leinster in the 2011 final at Cardiff, have also drawn French Top 14 champions Castres and RaboDirect PRO12 side Ospreys in what looks to be the toughest pool.
Reigning champions Toulon will face sides from England, Scotland and Wales as they must overcome Cardiff Blues, Glasgow and Exeter if they are to advance from Pool 2 as they bid to retain their title.
Saracens will face four-time Heineken Cup winners Toulouse, Connacht and Italian side Zebre in Pool three, while Aviva Premiership champions Leicester appear to have been given a favourable draw against Ulster, Montpellier and Treviso.
Clermont, who topped the French championship at the end of the normal season and were runners-up to Toulon in last season's competition, will meet Harlequins, Scarlets and Racing Metro in the only pool with two French teams.
Meanwhile, in Pool 6, two-time champions Munster will face Perpignan, who return to the premier European competition after a two-year absence, Edinburgh and Gloucester.