It was expected that Mr O'Gara, owner of Marble and Granite Tiles Ltd, would appeal against his winding-up order, but the time for this has expired.
"That now means there is no reversal of the liquidation," said Labour councillor Oisin Quinn.
Mr O'Gara drew controversy after he attempted to establish a series of business ventures on the south Dublin park including a car park and a tile showroom.
Previous caretaker Dublin City Council won a court application last October to wind up Marble and Granite Tiles.
The next move will be for the liquidator to put the square up for sale as a matter of protocol and in order to find the best price.
The proceeds from the sale will pay creditors, Dublin City Council, who are owed €43,000 in lieu of legal fees.
"Jim Hamilton has been appointed liquidator to wind up the company and dispose of the assets, Dartmouth Square," he added.
"He will put the square on the market to get the best price that he can."
But it is likely that the council will put in an offer for the property in a move that will technically wipe out debts owed to Dublin City Council.
"We as councillors have asked the manager to ensure that Dublin City Council will acquire the square," Cllr Quinn explained.
"The planning potential has been completely removed. There is no value other than a public square.
"It's hopefully the end to a complicated chess game," he said. "To be honest the only chess move left is sliding the queen into position."
Despite losing control of the land over four years, the exercise would have proved to be virtually "cost neutral" for the local authority, explained Cllr Quinn.
And the liquidator has said that he hopes that the situation will be concluded within a relatively short period of time.
This final move will usher in a new era of access for residents who have, along with volunteers, cleared the park of dead branches and soil to restore it to its former glory.
Over the summer, Dartmouth Square held yoga classes, poetry readings, film showings and concerts as the park was run as an amenity for locals.