The job is a major coup for the builder, which is understood to have agreed to use materials from Ireland wherever possible.
The new centre is at the heart of a 25 acre site complex at Queen’s Road including a world-class exhibition space.
Future plans include a hotel, fitness centre, playing fields and 250,000 sq ft of employment space.
Chairman of the IWHC Michael Forde said: “We have always planned to use Irish building materials. We want people to be walking on Irish wood and surrounded by Irish stonework.”
The new centre will celebrate the Irish disapora, the men and women who left Ireland over the centuries and have risen to become educators, entrepreneurs, entertainers and political leaders in many foreign countries.