Incoming Taoiseach Micheál Martin has hailed his new role as "one of the greatest honours which anyone can receive".
The Fianna Fáil leader was elected Taoiseach of the 33rd Irish parliament, with 93 TDs voting in favour and 63 against. Three TDs abstained.
Mr Martin used his inaugural speech to pay tribute to the health workers and those who have died in the Covid-19 pandemic.
He told the Dáil, sitting in Dublin's Convention Centre: "We are meeting away from our permanent chamber because of a historic pandemic which has struck Ireland and the rest of the world.
"As of today, 2,278 people on this island have lost their lives.
"Many thousands more have fought a long struggle to recover. There is no community, no part of our country, which has escaped untouched.
"In the last three-and-a-half months, enormous progress has been made in controlling the spread of the virus and treating those who have become sick.
"The struggle against the virus is not over. We must continue to contain its spread. We must be ready to tackle any new wave, and we must move forward rapidly to secure a recovery to benefit all of our people."
As he hailed the honour of being elected Taoiseach, Mr Martin paid tribute to his wife and children, and said he is proud of his working class roots.
He said: "Most of all I want to thank my family and my community. Without them I could have achieved nothing."
Detailed negotiations on an agreement on shared priorities with Fine Gael and the smaller Green Party have been delayed by the coronavirus crisis.
Firm targets for reducing carbon emissions and encouraging sustainable transport, as well as helping the country recover from economic harm caused by infection restrictions, will be among the new administration's priorities.
The Dáil met in the unusual surroundings of the glass-fronted convention centre on Dublin's River Liffey.
The temporary change of venue from Leinster House was to enable social distancing and to allow all 160 public representatives to sit.
Mr Martin is now meeting Irish President Michael D Higgins at Áras an Uachtaráin to receive his seal of office.
Ministers are also due to be appointed later on Saturday.
Mr Martin has taken over from Mr Varadkar in a historic reconciliation of a political feud with Fine Gael dating back to the foundation of the state a century ago.
Fine Gael are due to retrieve the Taoiseach's role at the end of 2022 under the terms of the coalition agreement.