Round one will see 1998 Heineken Cup winners Bath also on the road as they clash with French club Montpellier in Pool Four.
Clermont Auvergne, who won the European Challenge Cup in 1999, and 1997 Heineken Cup champions Brive both travel to face domestic opposition in tournament debutants Albi and Montauban respectively.
Tournament newcomers Newport Gwent Dragons host Bayonne in Pool One, Saracens face a visit by Glasgow Warriors in Pool Two, Newcastle host Petrarca Padova in Pool Three and Bristol host Romanian representatives Bucuresti in Pool One.
Pool 1: Newport Gwent Dragons, Bayonne, Bristol, Bucuresti.
Pool 2: Glasgow Warriors, Narbonne, Saracens, SKG Gran Parma.
Pool 3: Newcastle, Brive, Petrarca Padova, Montauban.
Pool 4: Connacht, Montpellier, Bath, Harlequins.
Pool 5: ASM Clermont Auvergne, Worcester Warriors, Arix Viadana, Albi.