The Belfast-based practice claimed the commission over burgeoning London practice Markland Klaschka, relative heavyweight Keppie Design, RHWL's Arts Team and Glasgow-based Cameron Webster Architects.
Practice partner Mark Hackett said: 'The Cathedral Quarter is crossed with narrow streets and little lanes, and we wanted to keep this character in our design.
'This is a significant result for us. We're a young practice - only just in our fourth year - and it is very difficult to get work of this size in Belfast as a small practice.'
Hackett and Hall beat more than 100 practices to win the competition, and will now work on detailed designs for the new facility.
When completed in summer 2011, the new facility will include two theatres, a visual arts space, dance studios, rehearsal rooms and a café.