Exeter will face French clubs Bourgoin and Montpellier and Premiership rivals Newcastle when they make their European bow in the Amlin Challenge Cup.
Gloucester also have two French sides in their pool - Agen and La Rochelle.
Leeds face Stade Francais, Rugby Parma and Romanian minnows Bucuresti, while Sale take on Brive, Italians Petrarca and Spanish side Cetransa el Salvador.
Harlequins tackle Irish province Connacht, French side Bayonne and Italians Cavalieri Prato in their pool.
The draw was conducted using the merit-based ERC European ranking system compiled on the qualified teams' performances over the past four seasons in the Heineken Cup and Challenge Cup knock-out stages.
This year's winners Cardiff Blues have qualified for the Heineken Cup along with beaten finalists Toulon.
Pool One: Harlequins, Connacht Rugby, Bayonne, Cavalieri Prato
Pool Two: Sale Sharks, Brive, Petrarca Rugby, Cetransa El Salvador
Pool Three: Bourgoin, Newcastle Falcons, Montpellier, Exeter Chiefs
Pool Four: Stade Francais Paris, Rugby Parma, Leeds Carnegie, Bucuresti Oaks
Pool Five: Gloucester Rugby, Agen, Rugby Rovigo, La Rochelle
Round One: 7/8/9/10 October, 2010
Round Two: 14/15/16/17 October, 2010
Round Three: 9/10/11/12 December, 2010
Round Four: 16/17/18/19 December, 2010
Round Five: 13/14/15/16 January, 2011
Round Six: 20/21/22/23 January, 2011
Quarter-finals: 8/9/10 April, 2011
Semi-finals: 30 April/1 May, 2011
Amlin Challenge Cup Final: 20/21/22 May, 2011