Warriors finished second in Pool 4, while the Tigers came third in Pool 1. The match will take place on either 4, 5 or 6 April at Scotstoun.
The other ties are Toulouse v Sale Sharks, Bordeaux v Ulster, Leinster v Harlequins, Northampton Saints v Clermont-Auvergne, Toulon v Saracens, Castres Olympique v Benetton and La Rochelle v Munster.
If Glasgow were to defeat Leicester, they would face the winners of Leinster v Harlequins in the quarter-finals.