The new Minister for Finance, Michael Noonan, has said the Government will restore the economy and create jobs - while also protecting the vulnerable in society.
He said it was unprecedented for the Taoiseach to have been elected by a majority of 90.
Mr Noonan said the reason the Government had been given a mandate by the public was that they offered hope, at a time when the other parties only offered negativity.
He said that Fianna Fáil, Sinn Fein and the Independents had talked of how they would oppose the new Government's policies, but none had produced even one idea of what should be done. He appealed to them to be more positive and to join in rescuing the country.
Earlier, Mr Michael Noonan had been named as the new Finance Minister by Taoiseach Enda Kenny.
Richard Bruton, from Fine Gael, was appointed Minister for Enterprise, Jobs and Innovation. Labour's Brendan Howlin got the new department of Public Expenditure and Reform.
Leo Varadkar is the new Transport, Tourism and Sport Minister while Joan Burton is the new Social Protection Minister.
Labour leader Eamon Gilmore is the new Tánaiste and was also named as Minister for Foreign Affairs and Trade.
Willie Penrose has been named as a super junior minister at the Department of the Environment with responsibility for housing and planning.
The full list of Ministers is as follows:
Eamon Gilmore - Tánaiste and Minister for Foreign Affairs and Trade
Michael Noonan - Minister for Finance.
Ruairi Quinn - Minister for Education and Skills.
Richard Bruton - Minister for Enterprise, Jobs and Innovation.
Frances Fitzgerald - Minister for Children
James Reilly - Minister for Health
Phil Hogan - Minister for Environment, Community and Local Government.
Leo Varadkar - Minister for Transport, Tourism and Sport.
Jimmy Deenihan - Minister for Arts, Heritage and Gaeltacht Affairs
Paul Keogh - Chief Whip
Alan Shatter - Minister for Justice, Equality and Defence.
Simon Coveney - Minister for Agriculture, Marine and Food
Joan Burton - Minister for Social Protection
Pat Rabbitte - Minister for Communications, Energy and Natural Resources.
Brendan Howlin - Minister for Public Expenditure and Reform
Willie Penrose - Super junior at Department of Environment with responsibility for housing and planning.