In a statement on Tuesday, Aiken Promotions said it was "with great regret" that no concerts would take place as planned.
It added: "The ticket return process will be outlined tomorrow (Wednesday).
"Aiken Promotions have exhausted all avenues regarding the staging of this event. We are very disappointed for the 400,000 fans who purchased tickets."
The country star was scheduled to play five sell-out gigs at Croke Park from 25 to 29 July, but Dublin City Council ruled that two could not go ahead.
Brooks responded to the news by saying there would be "five gigs or none at all".
The Council said its decision to reduce the number of concerts could not be amended or appealed, leaving thousands of fans in doubt as to whether or not they would get to see the star perform.
Following the cancellation announcement, Ticketmaster Ireland said it was "working on a plan" to refund the 400,000 fans who had bought tickets.
It added: "However the scale of this operation is unprecedented in the Irish entertainment industry and therefore we would ask customers to continue to be patient while we finalise our plan.
"Full details of the plan will be published in the coming days."
Meanwhile Translink have said they will be giving full refunds for any bookings for their rail and coach specials for the concerts.
The company also said they would confirm details in the next few days.
We are working on a plan to make the cancellation process as simple and convenient as possible for customers.
One angry fan, Mary Barr from Lisburn, told UTV she was "devastated" that she won't be getting to see Brooks perform, especially as she had planned to visit Dublin as part of her birthday celebrations.
She said: "You would imagine that when you pay your money, that's you, you are going to the concert. You never expect they are going to pull out.
"They were quite willing for people to buy these tickets, they were quite willing to let them put on as many gigs as they thought that he could fill. I just think it is very, very disappointing.
"We were going to make a weekend out of it...and going to make good memories out of it, but what have we now?...a bill for a hotel that we won't use, because I won't go down to Dublin and give them my money...I'm so angry."
The GAA said: "Croke Park Stadium has worked closely with Aiken Promotions in its efforts to stage a unique series of concerts which would have represented an exciting national event and a joyful summer celebration.
"From the outset Croke Park Stadium, as it does with the planning of all events staged in Croke Park, and with a view to avoiding surprise late difficulties, engaged fully with Dublin City Council officials and addressed comprehensively every issue presented during this planning process.
"At no stage were we given any indication that a licence was likely to be refused for any of the five concerts."
Aiken Promotions had been criticised for "recklessly" selling tickets and promoting the gigs without permission from the DCC to stage the concerts.
They released a statement on Monday night, saying that at all times they followed the process as laid down under the event licencing procedure.
It added: "While Council Officials may have followed a proper process, we believe that the decision was not correct.
"The demand for tickets for The Garth Brooks Comeback Special Event was unprecedented, selling almost one entire show to audiences from outside Ireland."
The statement continued saying that all discussions with Dublin City Council Officials in relation to the five concerts was about how the impact of all five concerts might be mitigated.
"Therefore the decision was a complete shock," the statement continued.
Garth Brooks' response to the licence for the three rather than the five concerts was not an ultimatum, it was simply an expression of genuine concern for his fans.
"Aiken Promotions has always acknowledged that five concerts would have an impact on the community. In our experience this impact is always reflected in the conditions applying to the licence, as it is in every event."
Last week Dublin City Council said it would not be appropriate to grant five consecutive nights of concerts at the GAA venue, considering three consecutive One Direction concerts had already taken place from the 23 to 25 May.
In a statement, it said: "Given that Croke Park is situated in a heavily populated residential area, five shows in a row following on from the three concerts already held there this year is considered an over intensification of use of the stadium for the holding of special events/concerts.
"It would be in effect permitting an increase of 100% in terms of the maximum number of concerts that had previously been held in Croke Park in any given year since the redevelopment of the stadium."
The Council said they also took into consideration the "cumulative effect on residents and on some businesses" in the area.
Residents living near Croke Park were last month handed £400,000 in compensation following a row over the upcoming concerts.
In January, Brooks announced his return to the venue after 17 years for two gigs, but huge demand for tickets meant three extra dates were added.
All five shows sold out immediately.
It would have been the first time that an artist played five consecutive sold out dates at Croke Park.