The Irish Greyhound Board (IGB) has agreed to sell Harold's Cross Stadium to the Department of Education for €23m.
In a statement, the IGB said the offer for the six-acre site was "in line with the market valuation".
The offer is subject to the approval of both the Minister for Agriculture and Minister for Public Expenditure and Reform.
Speaking at the Dáil's Public Accounts Committee earlier this month, IGB Chairman Phil Meaney said it did not make commercial sense to keep Harold's Cross open and that the market was not big enough to sustain two greyhound racing tracks in the capital that were so close to each other.
When it emerged the IGB was planning to sell the venue, one of two it has in the capital, the Dublin Greyhound Owners and Breeders Association (DGOBA) was strongly opposed to the move.
Protests by the DGOBA led to several race meetings behind cancelled at nearby Shelbourne Park, but Harold's Cross was closed in February.
The proposed sale is part of the implementation of the Indecon Report, which was commissioned by the Government and published in 2014.
The report recommended the sale of Harold's Cross in order to help tackle the IGB's debt, which now stands at over €20m.
Mr Meaney has previously said the decision "brings to an end to a long and sometimes difficult process to sell one of our Dublin stadiums, which makes commercial and operational sense for the IGB".
He added then the sale would be of huge benefit to the industry and "will allow us for the first time in many years, a capacity to invest in the many areas that require support and attention".
