Following the conclusion of the pool stages, Ulster will advance as the 16th ranked team and will therefore face an away trip to number 1 ranked side, Bordeaux.
The sides have already met in the pool stages, with the Frenchmen recording a bonus point win at Kingspan Stadium, as they did in each of their four pool stage games to top the Champions Cup standings.
The Round of 16 fixtures will take place over the weekend of 4/5/6 April, and ticketing information will be communicated in due course.
Investec Champions Cup
Round of 16 - 4/5/6 April
R16 1: Union Bordeaux-Bègles (1) v Ulster Rugby (16)<br>
R16 2: Leinster Rugby (2) v Harlequins (15)<br>
R16 3: Northampton Saints (3) v ASM Clermont Auvergne (14)<br>
R16 4: RC Toulon (4) v Saracens (13)<br>
R16 5: Stade Toulousain (5) v Sale Sharks (12)<br>
R16 6: Castres Olympique (6) v Benetton Rugby (11)<br>
R16 7: Glasgow Warriors (7) v Leicester Tigers (10)<br>
R16 8: Stade Rochelais (8) v Munster Rugby (9)
Quarter-Finals - 11/12/13 April
QF 1: Winner R16 1 v Winner R16 8<br>
QF 2: Winner R16 2 v Winner R16 7<br>
QF 3: Winner R16 3 v Winner R16 6<br>
QF 4: Winner R16 4 v Winner R16 5
Semi-Finals - 2/3/4 May
SF 1: Winner QF 1 v Winner QF 4<br>
SF 2: Winner QF 2 v Winner QF 3
Final - Saturday 24 May at Principality Stadium, Cardiff