Infrastructure Minister Nichola Mallon MLA said her decision marks a significant step in the redevelopment on its existing site on the Andersonstown Road.
Minister Mallon said: "The Ulster Council of the GAA can now move forward with their ambitious plans for the regeneration of the stadium.
"Since taking office I have stressed the need for progression of this long awaited application. I acknowledge that this approval was not an easy decision, there has been an extensive consultation process due to the complexities of the application and the level of public representation in relation to the proposal.
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"I recognise the impacts on residential amenity from the proposed development but ultimately I had to weigh such impacts with the social and economic benefits that would result from the completion of this project and I truly believe that the Casement Park stadium will be successful.
"The new stadium is of high quality design and will become a renowned landmark building which will provide a further catalyst for regeneration of the Andersonstown Road and an economic boost to West Belfast in general. Belfast as a whole shall benefit from this redevelopment, connecting people from across the city, the north and further afield.
"This stadium will boost sports tourism and the economy in the North. Jobs during the construction phase and additional jobs for the daily management are to be welcomed."
