Fine Gael had been threatening to withdraw co-operation in the Dáil if its extra number of TDs was not recognised with extra posts as Chair and Vice-Chair.
It now appears that the main Opposition party has been successful in this demand, although details have not been made public yet.
It is likely to take another week to ten days before the names of the holders of the offices will be confirmed.
One participant described the negotiations as 'lengthy and difficult'.
The Government was proposing the creation of 22 committees in the new Dáil, which the Opposition has claimed is far too many.
Fine Gael's Charlie Flanagan said this number was far too many for a House of 166 members. He said members would meet each other rushing from one to another, and claimed nobody would have any idea what was going on.
Former Labour leader Pat Rabbitte said the media would draw the conclusion that so many positions were being created so the Taoiseach, Bertie Ahern, could 'give a chocolate sweet' to disappointed aspirants for ministerial office.
Committee chairpersons get an extra allowance of almost €20,000, while each Committee also has a vice-chairperson and a convenor who is paid extra.
Earlier, Tom Kitt confirmed that there will be new Oireachtas committees.
In statements to the Dáil this morning he said the Government would be establishing a Committee on the Constitutional Amendment regarding Children, which is expected to be put before the people next year.
There will also be a Committee on the Implementation of the Good Friday Agreement.
However, Mr Kitt said negotiations on Dáil reform had been fruitless because of what he said was the Opposition's pre-occupation with the number of weekly appearances the Taoiseach made in the house.
Fine Gael leader Enda Kenny said parliamentary committees are institutions of the Dáil and not of Government.
Mr Kenny said deputies were reluctant to spend three or four hours in a committee when that work will never see the light of day.
Mr Kenny said there was no technological reason why proceedings in Dáil, Seanad and in committees should not be broadcast on a parliamentary channel, and that there was always someone to watch it.
On the question of a Committee on the Good Friday Agreement, which would allow elected representatives from the North to speak, he said it was ironic that they were talking about allowing MPs who do not attend Westminster to come to committees in Leinster House, and said it was important to ensure that politicians from all sides were in favour of the development.
