Taoiseach earlier announced Senator Jerry Buttimer as Fine Gael leader in the Seanad
Fianna Fáil's Denis O'Donovan has been elected Cathaoirleach of the new Seanad.
He was elected with support from Fine Gael and independents, as well as his own party.
The appointment of Senator O'Donovan means both the Dáil and Seanad are chaired by members of Fianna Fáil.
The position was also contested by Sinn Féin's Rose Conway-Walsh, something the new Cathaoirleach says is important.
The 60 new senators, who make up the 25th Seanad, are meeting for the first time in Leinster House this afternoon.
The 25th Seanad is meeting for the first time this afternoon.
It has already cost the taxpayer hundreds of thousands of euro in wages and expenses before holding a single sitting.
Earlier today the Taoiseach announced Senator Jerry Buttimer as Fine Gael leader in the Seanad.
The announcement came following earlier speculation former Minister James Reilly would be the leader of the party in the upper house.
In a statement, Enda Kenny said: "Jerry has gained considerable parliamentary experience as senator, Dail deputy and as chairperson of the Joint Oireachtas Committee on Health.
"This experience makes Jerry very ably qualified for what will be a very important and challenging role in the new parliamentary environment."
The 'Upper House' of the Oireachtas is now due to adjourn again for a week.
Meanwhile, a group of Independent Senators say they are "taking the Seanad back" after it was 'hijacked' by the political parties in 1937.
The 10 Independents and one Green Party senator have put forward a bill that would reform the upper house of the Oireachtas - including giving every person born in Ireland a vote.
Senator Gerard Craughwell says from today on, the reform begins.
"We intend to make this Seanad work - I think you are going to find this is a very interesting Seanad, a very interesting term," he said ahead of today's meeting.
The longest-serving member of the house, David Norris, warned about the perils of Seanad reform and spoke against allowing all citizens to vote in university panels, without reforming other panels.
He said "it would lead to a constituency of 850,000 to one million voters" and therefore eliminate "the independent voice and leaving the way open to invasion by political parties."