Varadkar, 38, will officially take over as Taoiseach, as the Irish prime ministerial title is known in Ireland, in Parliament later this month after he was declared the victor in the leadership race for the Fine Gael party.
Varadkar, the son of an Indian-born father and Irish mother, became a doctor before first entering Irish parliament at the age of 27.
The 38-year-old leader became the first openly gay Cabinet minister in Ireland after coming out in 2015.
Sean Spicer 'fuming' after getting axed from Trump's Papal visit, says source
The Pope Francis gave Donald Trump a medal featuring an olive branch , a symbol of peace, among other gifts. Melania and Ivanka wore conservative black dresses and veils during their trip to the Vatican.
A member of Fine Gael since he was a teenager, he took 60 per cent of votes in the leadership contest, while Coveney, housing minister and his only rival, took 40 per cent.
Enda Kenny, the former PM of Ireland, stepped down this earlier this week as leader of the Fine Gael party after ruling the country for six long years.
LEO Varadkar declared yesterday that "prejudice has no hold on this republic" after he was elected the new leader of Fine Gael.
Does Trump Believe In Climate Change? White House Won't Say
But countries like China and India are far behind the USA economically and can't match its ability to invest in clean technology. He didn't sound at all concerned about the fate of the planet Thursday when he announced his decision to leave the agreement.
Within the rules of Fine Gael, the party's MPs, members and MEPs vote on their leader. Its piece details again how the gay son of an Indian immigrant is set to take the role of taoiseach. But, Varadkar himself pointed out, Sebastian Kurz, the favourite to become Austria's new prime minister, is eight years younger. Fine Gael means "Tribe of the Irish", and the party is considered liberal-conservative with Catholic leanings.
"It is not something that defines me".
Varadkar, 38, also would be the Republic of Ireland's youngest prime minister ever. "It is a great moment of pride for our country that Leo is going to be the Prime Minister of Ireland". "It is a sign of how much Ireland has changed and moved on that no one really cares if he is gay here. It is just part of who I am, it does not define me, it is the part of my character I suppose".
Trump pulling US from global climate pact, dismaying allies
The source, speaking on condition of anonymity, said Trump was working out the terms of the planned withdrawal with U.S. Environmental Protection Agency Administrator Scott Pruitt , an oil industry ally and climate change sceptic.