Varadkar, officially took over from Enda Kenny as Taoiseach, as the Irish prime ministerial title is known, after a parliamentary vote confirmed him as the leader by 57 votes to 50, with 47 abstentions.
The former general physician, who is the son of an Irish nurse and a doctor from India, won the Fine Gael party leadership earlier this month. He has made his leadership rival Simon Coveney the deputy leader of the party.
"The government that I lead will not be one of left or right because those old divisions don't comprehend the political challenges of today. The government I lead will be one of the new European centre as we seek to build a republic of opportunity," Varadkar asserted.
He then travelled to the president's residence, Aras an Uachtarain, where President Michael D Higgins gave him the seals of office to officially confirm his appointment.
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Former Taoiseach Kenny nominated Varadkar to succeed him at the start of today's Dail proceedings, saying that he would carry out the role with integrity and skill.
"He (Varadkar) represents a modern, diverse and inclusive Ireland and speaks for them like no other, an Ireland in which each person can fulfil their potential and live their dreams," Kenny said.
After winning the party leadership earlier this month, Varadkar had said, "If my election shows anything it's that prejudice has no hold in this Republic."
"When my father travelled 5,000 miles to build a new home in Ireland, I doubt he ever dreamed his son would grow up to be its leader," he had said.
Varadkar went up against housing minister Coveney in the leadership race, who bagged two-thirds of the party membership votes but lost out to the more popular candidate in the end.
Varadkar came out as a gay man in 2015, when Ireland became the first country in the world to legalise same-sex marriage through popular vote.
In a coming-out speech he gave in a radio interview, he had said, "It's not something that defines me. I'm not a half-Indian politician, or a doctor politician or a gay politician for that matter. It's just part of who I am, it doesn't define me, it is part of my character I suppose."
His partner, Matthew Barrett, is also a doctor.
"Matt is just a very special person. Someone who is unconditionally on my side, which is always great. He is the kind of person who has made me a better person," Varadkar recently said.
The popular minister has campaigned for same-sex marriage and liberalising abortion laws.
He worked as a general practitioner (GP) before winning a seat in Parliament in 2007 and has rapidly risen through the party ranks, holding several ministerial portfolios including minister for social protection and minister for transport, tourism and sports.
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