The one-legged tie will take place in Paris on the weekend of April 9-10-11.
It’s a really tough draw for Richard Cockerill’s side against last season’s European Cup runners-up who boast a formidable array of talent.
Scotland stand-off Russell pulls the strings in a backline which also includes Simon Zebo, Juan Imhoff and Virimi Vakatawa.
If Edinburgh can overcome the French giants they will face either Bordeaux-Begles or Bristol Bears in the quarter-finals on the following weekend.
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Holders Exeter will face Lyon at home in the last 16 while the tie of the round is arguably Munster v Toulouse.
Heineken Champions Cup last 16
Munster v Toulouse
Gloucester v La Rochelle
Wasps v Clermont
Exeter v Lyon
Leinster v Toulon
Bordeaux-Begles v Bristol Bears
Racing 92 v Edinburgh
Scarlets v Sale
Heineken Champions Cup quarter-finals
Exeter or Lyon v Leinster or Toulon
Wasps or Clermont v Munster or Toulouse
Gloucester or La Rochelle v Scarlets or Sale
Bordeaux-Begles or Bristol Bears v Racing 92 or Edinburgh
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