Former internationals Simon Shaw and Scott Quinnell carried out the inaugural draw at the Stade de la Maladière in Neuchatel, Switzerland and pitted the Chiefs in Pool Two of the 2014/15 competition.
Standing in the way of Rob Baxter's side will be French Top14 sides Bayonne and La Rochelle, as well as Rabo ProDirect12 outfit Connacht Rugby.
The Chiefs have previously faced Connacht in two pre-season friendlies, but have never before faced either Bayonne or La Rochelle.
"It's a terrific draw for us," said Exeter Rugby Club's chief executive Tony Rowe OBE. "Obviously we have played Connacht before, both here at Sandy Park and over in Galway, but we've never faced either of the two French clubs.
"As a club we always enjoy facing the challenges of Europe and this season will be no different for us. In the past few years we have enjoyed some memorable trips across Europe and I've no doubt that many of our supporters will already be busy planning potential trips across the water."
Confirmation of the fixture dates is set to follow next month from European Professional Club Rugby.
