The theatre was controversially earmarked for demolition under Will Alsop's city-centre masterplan - a move that sparked local outrage.
Now the Bradford Centre Regeneration (BCR) company wants to build 'an iconic new building' on the plot in Princes Way.
Maud Marshall, BCR's chief executive, said: 'The purpose of the competition is to get the best for the city from the development of this landmark site.
'We do not intend to be prescriptive in our brief to the developers and will not be advocating any one particular option.
'What matters is that Bradford gets a building, the design and functions of which reflect the city's dynamism and talent, while complementing the richness of its architectural heritage.
'We will be inviting teams of architects and developers to express an interest in getting involved in the process. A shortlist will then be compiled based on the track record and financial capacity of the organisations concerned,' she added.
For more information about the competition call Lindsey Ramsay or Ruth Pagett on 0113 220 0508.