Wates is working with architects Strategic Design Alliance – a partnership of Jacobs Architecture and the council’s in house architects - to develop the design proposals.
The project is the result of £10.5 million of funding raised by the Council, Arts Council England and Yorkshire Forward. NBT and Phoenix are campaigning to raise the final £1.5 million.
The contractor will be confirmed towards the end of the year with work set to start in spring 2009. Completion is set for summer 2010.
Leeds City Council deputy leader Andrew Carter said: "This is an important step forward in our vision to put Leeds on the map as a national and international centre of excellence for dance, and provide a fitting home for our two renowned dance companies.”