Reigning Heineken Cup champions Exeter face a round-of-16 date with Lyon and a potential heavyweight quarter-final clash against either Leinster or Toulon at Sandy Park.
The Chiefs discovered their European opponents as the competition's revised knockout phase saw two draws made in Lausanne, Switzerland.
Leinster and Toulon have seven Champions Cup titles between them, with the Irish province having won four European crowns and the French club three.
Two-time winners Wasps were the only English club guaranteed home advantage after winning both pool games on the field, with results not impacted by Covid-19.
Wasps, winners in 2004 and 2007, will host Clermont Auvergne with the winners playing Munster or four-time winners Toulouse at home in the last eight.
Bristol will travel to Bordeaux-Begles in the last 16, the Bears having beat the French side on their way to win the Challenge Cup in 2020.
The winners will be at home to Racing 92 or Edinburgh in the last eight.
Gloucester welcome La Rochelle to Kingsholm in the round of 16 and victory will secure a home tie against either Scarlets or Sale, who must head to west Wales for their knockout clash.
The pick of the Challenge Cup last-16 ties sees Ospreys host Newcastle and the Dragons entertain Northampton.
Cardiff Blues, tournament winners in 2018, travel to London Irish and Bath visit Zebre in Italy.
The draw for the quarter-finals were also made in Lausanne and there are three potential all-Gallagher Premiership ties.
Northampton-Harlequins, Bath-London Irish and Leicester-Newcastle are all possible last-eight clashes.
The rounds of 16 will be staged from April 2-4 with the quarter-finals set for the following weekend on April 9-11.
Full draw
Champions Cup round of 16: Munster v Toulouse, Gloucester v La Rochelle, Wasps v Clermont Auvergne, Exeter v Lyon, Leinster v Toulon, Bordeaux-Begles v Bristol, Racing 92 v Edinburgh, Scarlets v Sale.
Champions Cup quarter-final: Exeter or Lyon v Leinster or Toulon, Wasps or Clermont Auvergne v Munster or Toulouse, Gloucester or La Rochelle v Scarlets or Sale, Bordeaux-Begles or Bristol v Racing 92 or Edinburgh.
Challenge Cup round of 16: Dragons v Northampton, Ospreys v Newcastle, London Irish v Cardiff, Harlequins v Ulster, Benetton v Agen, Zebre v Bath, Leicester v Connacht, Montpellier v Glasgow.
Challenge Cup quarter-final: Montpellier or Glasgow v Benetton or Agen, Dragons or Northampton v Harlequins or Ulster, Zebre or Bath v London Irish or Cardiff, Leicester or Connacht v Ospreys or Newcastle.
