Nichola Mallon has said she is recommending approval for the long-awaited redevelopment of Casement Park.
The infrastructure minister she had "carefully considered" all of the representations and it had been a "complex application".
Some west Belfast residents have consistently objected to the scale of the development of the GAA stadium.
Ms Mallon said she was aware of more than 1,000 objections to the most recent planning application.
She said she had "carefully weighed" the concerns of residents against "everything else" the stadium's construction could bring to the area.
"When you have an application of this size and when you have a stadium being constructed within a residential area, there will of course be many concerns," she said.
"There are a number of conditions on the application to try and address resident concerns."
Today I have announced that I am recommending Casement for approval. I believe this landmark stadium will be transformational in sporting, social & economic terms for Ulster & our island. pic.twitter.com/OCkWBgbav8— Nichola Mallon (@NicholaMallon) October 13, 2020
The minister said it would transform Gaelic games and the economy of west Belfast.
"I believe it will be truly transformational in sporting terms and economic terms for the whole of Ulster," she said.
Casement Park Stadium development project board chairman, Tom Daly, said the project would "bring with it many direct and indirect jobs along with increased revenues for local businesses and the regeneration of the area".
Ulster GAA said 95% of those who took part in the 32-week-community consultation said they were in favour of the new design.
Ulster GAA chief executive Brian McAvoy thanked members and the wider GAA community for their "patience and continued support throughout this journey".
"The redeveloped Casement Park will bring positive local community benefits and we will work hard to be a good neighbour for all those who live in the locality," he said.
Analysis: A big step forward
By Mark Simpson, BBC News NI
The proposed new stadium will be the biggest in Belfast.
With room for more than 34,000 spectators, its capacity is almost double the size of Windsor Park and the Kingspan Stadium.
The project has been in the pipeline for more than a decade and it is still not guaranteed.
There could yet be a legal challenge. Some local residents claim the proposed new stadium is simply too big for a heavily populated area.
There are also questions about exactly how the multi-million pound project is going to be funded.
But as things stand, the chances of the new Casement Park finally being built are now high.
The initial cost of the new Gaelic Athletic Association (GAA) stadium was estimated at £77m.
In March 2019, the Department for Communities (DfC) said the sharp rise in cost meant it could not give the go-ahead, even with planning permission, because of a lack of a minister at Stormont.
In January 2020, the GAA said planning authorities had indicated they were "hopeful" the process could come to an end, possibly by early April 2020.
On Tuesday, Deputy First Minister Michelle O'Neill welcomed Ms Mallon's decision, saying it was a "great result".
First Minister Arlene Foster said she hoped to see her native county of Fermanagh in an Ulster final at the new Casement Park.
Responding to a question in the assembly, the DUP leader said she looked forward to receiving a invitation.
The initial proposals for the redevelopment of the stadium collapsed in 2014 under a legal challenge brought by a group of residents.
A fresh planning application was submitted in February 2017.
The new stadium has a proposed capacity of 34,186 - down from the GAA's original plan of 38,000.
The GAA said height, scale and capacity were all reduced from the previous design and that it was aiming to work within the original budget of £76m.
The infrastructure minister's decision follows a change in the law which clarifies when a minister can make an autonomous decision rather than having to seek wider executive approval.
The legislation was changed after a court ruling on the Arc21 incinerator project in 2018, which meant every major planning decision would have to come to the executive.