The project will enable major theatrical productions, community and amateur performances and arts education programmes to be held under one roof.
RHWL arts team partner Barry Pritchard said the scheme, to be built next to the opera house, will create a "new theatre experience".
He said: "Our intention is to dissolve the boundaries between performance and foyers. We want to create freer forms that play with the senses to create marvellous theatricality."
The practice beat rivals Allies and Morrison, Building Design Partnership, Burrell Foley Fischer and Glenn Howells Architects.