It is expected that Fianna Fáil's Denis O'Donovan will be elected Cathaoirleach of the 25th Seanad when it meets for the first time tomorrow.
Significantly, this will mean that Fine Gael will back him in the vote for the prestigious role usually held by a Government senator.
Senior sources within both parties have indicated tonight that they have just reached an agreement on the matter.
It is a sign of the much talked about new politics in Leinster House that is underpinning the minority Government.
It is anticipated that Fianna Fáil would then support Fine Gael's Paul Coughan to become Leas Cathaoirleach when a vote is held to fill that role next week.
Fine Gael will also have to choose a leader in the Seanad.
It was widely expected that Taoiseach Enda Kenny would appoint the party's deputy leader and former health minister, Dr James Reilly to this role.
However, the indications tonight are that this will not happen.
Former TD Jerry Buttimer is now favourite to get the high profile position.
The names of two others from Fine Gael who lost their seats in the General Election, Paudie Coffey and Kieran O'Donnell, have also been mentioned.
The House will also be addressed tomorrow by the longest serving Senator David Norris.
Sinn Féin has a motion down that calls for a special committee to swiftly come up with recommendations to reform the house.
The party wants the committee to be established within the next fortnight and to report four weeks after that with firm proposals.
These could include the role of a reformed Seanad and plus any legislation needed to give it new powers.
The Programme for Government has committed to implementing the Manning Report on Seanad reform.
It recommended that a majority of the 60 Senators should be elected by popular vote.
And it said the Seanad could investigate matters of public policy and consider reports from regulators.