Richie Murphy's side travel to France to take on the TOP14 high-flyers after Round 4's 52-24 victory over Exeter Chiefs at Kingspan Stadium booked the province's spot in the last 16 of European rugby's premier competition.
Both sides met earlier in the Pool stage, with Bordeaux winning 19-40 at Kingspan Stadium in Round 2.
Ticketing details will be communicated when confirmed by the host club.
Union Bordeaux Bègles v Ulster Rugby, Round of 16, Investec Champions Cup, Sunday 6 April, 1.30pm (local time), Stade Chaban-Delmas (Live on Premier Sports)
Round of 16 - Investec Champions Cup (Pool stage rankings in brackets / All kick-offs local times)
Friday 4 April <br>
Match 3: Northampton Saints (3) v ASM Clermont Auvergne (14), cinch Stadium @ Franklin’s Gardens (20.00) <br>
Premier Sports / beIN SPORTS / SuperSport / FloRugby
Saturday 5 April <br>
Match 4: RC Toulon (4) v Saracens (13), Stade Félix Mayol (13.30) <br>
beIN SPORTS / Premier Sports / SuperSport / FloRugby
Match 2: Leinster Rugby (2) v Harlequins (15), Croke Park (15.00) <br>
RTE / Premier Sports / beIN SPORTS / SuperSport / FloRugby
Match 6: Castres Olympique (6) v Benetton Rugby (11), Stade Pierre-Fabre (16.00) <br>
beIN SPORTS / France TV / EPCRugby.TV / PremierSports / SuperSport / FloRugby
Match 8: Stade Rochelais (8) v Munster Rugby (9), Stade Marcel Deflandre (18.30) <br>
beIN SPORTS / PremierSports / SuperSport / FloRugby
Match 7: Glasgow Warriors (7) v Leicester Tigers (10), Scotstoun Stadium (20.00) <br>
Premier Sports / beIN SPORTS / SuperSport / FloRugby
Sunday 6 April <br>
**Match 1: Union Bordeaux-Bègles (1) v Ulster Rugby (16), Stade Chaban-Delmas (13.30) <br>
*beIN SPORTS / PremierSports / SuperSport / FloRugby***
Match 5: Stade Toulousain (5) v Sale Sharks (12), Stadium Municipal de Toulouse (16.00) <br>
France TV / beIN SPORTS / Premier Sports / SuperSport / Flo Rugby