Environment Minister Mark H Durkan has approved the major multi-million pound redevelopment despite over 1,000 residents objecting to the plan.
Mr Durkan said: "Planning approval will now lead to the creation of a modern sports stadium with improved facilities and increased spectator comfort.
"The new stadium is a high quality design which will be a recognised landmark building which will assist with the ongoing regeneration of the Andersonstown Road and boost the city of Belfast.
"This stadium will have the potential to host cross-provincial matches usually played at Croke Park or Clones.
"This 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."
This is a tremendous boost for Gaelic games and for sport here.
Mark H Durkan
The decision, he said, had not been an easy one.
Mr Durkan's department received around 984 objections and a petition of objection with 431 signatures.
Planners also received 254 letters in support of the plan and another petition with 1,001 signatures welcoming the development.
The project is expected to cost close to £80m.
During the official announcement at the stadium a number of people staged a demonstration voicing their concerns over the development.
One resident told UTV: "It does need to be redeveloped of course and we are supporting that.
"But we do not need it to be that size and that is what we are against.
"So the fallout from that then comes the issue with traffic and the footfall in this area."
This whole area is going to be gridlock.
Minister Durkan said he had met with local residents and understood their concerns about the impact of the proposal.
"As Environment Minister for the whole of the north, my decision cannot ignore the regional benefits that will result from the development of this stadium and how it fits with the Executive's programme for government," he said.
"The future management of events is key to the success of the stadium and I expect the GAA to honour their commitment to help ensure that a vibrant stadium can exist within and for the benefit of the local community and indeed all of Northern Ireland.
"I believe this proposal can build a better environment and a stronger economy."
Ryan Feeney from the GAA's Ulster Council said he was delighted to have reached the latest milestone in the project.
He told UTV: "We are very pleased to have reached this stage in the planning process.
"The process is there to adjudicate and to ensure the rights of all those involved, both the GAA and those living locally, were taken into account before a planning application was approved.
"We are building on the current Casement Park 12 acre site.
"We have done as much as we can to accommodate and ensure that the design of the building and the planning application matches the needs of the local area.
"So we are pleased to have reached this milestone."
We have more work to do, but all in all it is a good day for the GAA.
The GAA has struck an agreement with Translink and other transport providers to help fans get to and from the games at the new facility and ease traffic congestion.
Ryan added: "What the GAA want to do is ensure people come and stay overnight in Belfast.
"So if there is a big game on a Saturday or a Sunday, then the people will get the experience of the second city.
"That will be a big focus of our marketing campaign and will hopefully provide a boost to the surrounding area and the hospitality industry."
Mr Feeney said he was confident the stadium could be filled regularly following its completion.
He added: "This is about meeting the strategic need of Gaelic games in Ulster.
"In terms of big games, while we have three at a minimum. We are intending to bring major GAA fixtures to Ulster and that has been our overall commitment.
"We as a province currently can't bid to host an All-Ireland quarter-final, we don't have the capacity or a stadium fit for purpose.
"But we have already had positive indications from Croke Park that it could happen.
"This year we had 8,000 more people who wanted to see the Ulster final but couldn't because Clones had a reduced capacity.
"We are also looking at semi-finals, double headers and ticket prices and in the past two years we have seen attendances in Ulster increase.
"So we are confident the stadium will be filled."
Northern Ireland Sports Minister Caral Ni Chuilin also welcomed the decision.
She said: "Having planning approval granted for Casement Park is the final part of the jigsaw in the regional sports stadium programme.
"Not only is this a tremendous boost for the GAA in Ulster, the redevelopment of Casement will bring many benefits to the community in west Belfast through construction jobs and a catalyst for regeneration in the area around the stadium."
The Stormont executive has pledged £110 million funding for the redevelopment of the three sports stadiums in the city at Ravenhill, Windsor Park and Casement.