Following a special parliamentary hearing on Saturday, Mr Martin, whose party won the most seats in February’s inconclusive election, was sworn in as the 33rd prime minister of Ireland.
Under the terms of the coalition deal, Mr Martin will only be in his role as leader for two and a half years, before the baton is passed back to Fine Gael.
Mr Martin’s accession to Taoiseach culminates more than 30 years in mainstream political life for the 59-year-old.
Speaking after being elected, Mr Martin said to be elected to serve as Taoiseach “is one of the greatest honours which anyone can receive”.
He 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. My wife Mary has been a pillar of support and a partner for me since our days in college.
“Our children have tolerated my many absences over the years. As they have grown, studied and experienced the world they have not just supported me, they have given Mary and I the benefit of their views of the Ireland which they have grown up with.
“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 Dail Eireann.
“Every day my parents showed us the importance of supporting each other, of tough but fair competition, and of the spirit of community.”
Mr Martin will take over the role of Irish premier from Leo Varadkar in an historic reconciliation of a political feud with Fine Gael dating back to the foundation of the state a century ago.
Fine Gael and Fianna Fael needed the support of the Greens to have a working majority in the Irish parliament, equating to around 80 seats, underpinning an extended period in office.
After weeks of talks, proposals on coalition were put to party memberships and results declared on Friday.
Fine Gael resoundingly endorsed them with 80 per cent in favour. Fianna Fail recorded 74 per cent.
The Greens’ support was the subject of speculation as it consulted its members but 76 per cent decided in favour. .
Among the first tasks of the Irish Government will be to renew legislation enabling the non-jury Special Criminal Court to continue dealing with serious organised crime in the Republic.
The effect of Brexit and rebuilding an economy plunged by the virus into what some commentators believed will be one of the worst ever recessions will also be pressing challenges.
Sinn Fein won the popular vote in last winter’s proportional representation election through an appeal to the young and buoyed by anger at the cost of housing and flaws in the health system.
It did not run enough candidates to fully translate votes into seats and was unable to form a “coalition of the left” with other parties of similar views but will now lead the opposition.