Fianna Fáil has returned to power for the first time in nine years, with Michéal Martin officially elected as Taoiseach.
Mr Martin described his election as Taoiseach as "the greatest honour that any Irish person could hope for."
He said: "I am humbled by the responsibility and I pledge to work night and day with my partners in Government to realise the great potential of our nation."
Mr Martin told the Dáil that his would be a government focused on rapidly delivering jobs.
"The challenges we must overcome are both immediate and, in many cases, long-standing. They can only be met and overcome if we work together across our responsibilities.
"There is no question about our first priority – continuing the fight against the Covid-19 pandemic and moving decisively to recover from its devastating social, economic and cultural impact.
"We will immediately begin the work of preparing an investment-led, jobs and recovery initiative which will be brought to the Dáil for approval next month. This will be a whole-of-government initiative about more than just the enormous task of getting our people back to work."
Mr Martin paid tribute to his children and his wife, Mary. He said that he personally had grown up in a "close-knit" family.
"I was blessed to be born into the home which my late parents created for me and my brothers and sisters in the heart of the close-knit, working-class community which I have the enormous privilege of representing in Dáil Éireann.
"Every day my parents showed us the importance of supporting each other, of tough but fair competition and of the spirit of community.
"From my late father we learned not just of the great sporting achievements he saw, we learned of the characters and values of the heroes who were and remain immortal to us.
However, the party's big day has been clouded by anger and confusion within the party towards Mr Martin's Cabinet appointments.
The Taoiseach opted to elevate Stephen Donnelly, who has only been a Fianna Fáil member since 2017, to the role of Minister for Health and overlooked his own Deputy Leader Dara Calleary, instead naming him Chief Whip.
Party sources said that while there was sympathy for other party figures who did not get appointed to Cabinet such as Thomas Byrne, Jim O'Callaghan and Anne Rabbitte, there was "shock" and "anger" about Mr Calleary's omission.
"It's hard to stomach when you consider that someone who's put in huge work for the party from when we had 20 TDs to now isn't at Cabinet and someone who joined in 2017 is," said one TD.
Mr Martin will be joined in government by his party colleagues Michael McGrath, Norma Foley, Stephen Donnelly, Darragh O'Brien and Barry Cowen, who will take the Public Expenditure, Education, Health, Housing and Agriculture portfolios respectively.