Sarries beat Racing 92 in the final of Europe's premier club competition last month and went on to complete a double by sealing the Premiership title.
Mark McCall's side will face a Toulon team looking for a positive response to a disappointing season in which they missed out on a fourth successive European title and were beaten by Racing in the Top 14 final.
Sale Sharks and Scarlets face the daunting task of coming up against Sarries and Toulon in Pool Three.
"It's an exciting pool against some extremely tough sides," said Sarries' director of rugby Mark McCall.
"Toulon have a star-studded squad who will have the extra hunger of not winning a trophy last season. We have faced them in the final stages of the tournament in recent seasons and we know how much of challenge they pose.
"The Scarlets have made some huge strides under Wayne Pivac and facing them at the Parc y Scarlets is always a test for teams in Europe. They have recruited extremely well this summer, bringing in some star names to add to an already competitive group, and have a backline that will threaten any side in the competition.
"Having played Sale Sharks a number of times over the last three seasons, in both the Aviva Premiership and the Champions Cup, we understand how dangerous they are.
"They have a great blend of youth and experience in their group and they are the most improved Premiership side over the last few seasons."
French champions Racing have been drawn in Pool One along with Leicester Tigers - who they beat at the semi-final stage this year - Munster and Glasgow Warriors.
Wasps, beaten by Sarries in the semi-finals in April, will take on Toulouse, Zebre and Connacht and Pool Two, while three-time European champions Leinster will take on Challenge Cup winners Montpellier, Northampton Saints and Castres in Pool Four.
Pool Five comprises of Clermont Auvergne, Bordeaux-Begles, Exeter Chiefs and Ulster.
Meanwhile in the Challenge Cup, this year's runners-up Harlequins will face Edinburgh, Stade Francais and Timisoara Saracens in Pool Five.