The Taoiseach, Bertie Ahern, has named Brian Lenihan, John Gormley and Eamon Ryan among his new Cabinet.
The full list is:
Brian Cowen - Tánaiste, Minister for Finance
Mary Harney - Minister for Health and Children
Mary Coughlan- Minister for Agriculture, Fisheries and Food
Seamus Brennan - Minister for Arts, Sport & Tourism
Noel Dempsey - Minister for Transport and the Marine
Éamon Ó Cuív - Minister for Community Rural and Gaeltacht Affairs
Willie O'Dea - Minister for Defence
Mary Hanafin - Minister for Education and Science
Micheál Martin - Minister for Enterprise, Trade and Employment
John Gormley - Minister for the Environment, Heritage and local Government
Dermot Ahern - Minister for Foreign Affairs
Brian Lenihan - Minister for Justice, Equality and Law Reform
Martin Cullen - Minister for Social and Family Affairs
Eamon Ryan - Minister for Communications, Energy and Natural Resources
Attorney General - Paul Gallagher SC
Mr Ahern earlier received his seal of office from President Mary McAleese at Áras an Úachtaráin after being elected Taoiseach for a third successive term.
At the first meeting of the 30th Dáil this afternoon, a vote to elect the Taoiseach saw Mr Ahern receiving 89 votes to Enda Kenny's 76.
He is now the first Taoiseach since Eamon De Valera to win three elections in a row.
Mr Ahern was nominated as Taoiseach by Fianna Fáil deputy leader Brian Cowen, a choice that was seconded by outgoing Green Party leader Trevor Sargent.
Progressive Democrats leader Mary Harney and Independent TD Jackie Healy Rae were among those who also lent their support to Mr Ahern.
Fine Gael Deputy Leader Richard Bruton nominated Enda Kenny for Taoiseach, a nomination that was seconded by Labour leader Pat Rabbitte.
While Sinn Féin's Caoimhghín Ó Caoláin told the Dáil that his party would not support the nominations of Bertie Ahern or Enda Kenny.
Earlier, John O'Donoghue was elected as Ceann Comhairle after defeating the former Labour leader, Ruairi Quinn, by 90 votes to 75.
Greens back Govt deal
Confirmation that the Green Party would join the new coalition came last night, when a special convention voted by more than 86% to accept the proposed programme for Government.
The new Government will be made up of Fianna Fáil, the Greens and the PDs, and will be supported by a number of Independents.
It gives Mr Ahern a comfortable majority, and insurance against any difficulties ahead.
The Green Party's negotiators admitted that the proposed Government programme was far from perfect from their point of view, with failures to secure movement on issues like the use of Shannon Airport by the US military, the building of the M3 motorway through the Tara valley, and hospital co-location.
But there will be two Green cabinet ministers, as well as two junior ministers, to implement the party's policies.
After the vote Trevor Sargent, who had strongly supported going into Government, said he was standing down as Green Party leader, as promised. He said he would not accept a cabinet post, but would accept a junior ministry if it was offered.
Click here to read Sargent leads the Greens into Government
Tension v responsibility
Ciarán Cuffe, Green Party TD, has said he believes there will be a huge amount of tension within the new coalition Government.
Speaking on RTÉ Radio's Morning Ireland, Mr Cuffe said the Green Party in Ireland had been advised by Green parties in government elsewhere in Europe to have a clear list of deliverables and not to walk out the moment tensions rise.
He said, however, that these tensions could be overcome.
He said the coalition brings together two parties; one very pragmatic and the other idealistic. He said both parties would bring a lot to the next Government, although sparks would be flying at times.
Fianna Fáil's Séamus Brennan has said larger parties in coalitions have an enormous duty not to use that strength to ride roughshod over smaller parties.
He added that smaller parties have a responsibility not to use their special position to give in to issues.