"He represents a modern, diverse and inclusive Ireland and speaks for them like no other, an Ireland in which each person can fulfill their potential and live their dreams", said Kenny, according to the BBC.
"His skill at avoiding hard news and distancing himself from the controversies of a government he sat in was remarkable".
Given that he has inherited a number of challenging problems it will take some time to see whether or not Leo Varadkar's Government can handle the pressures of sustaining an ever changing Ireland and it's people.
Global reaction to the election of Leo Varadkar as Taoiseach has largely focused on his sexuality.
He will address the Dail chamber just after 2pm and announce that he will head to Aras An Uachtarain to formally hand in his resignation to President Michael D Higgins.
After the election, the center-right politician promised the Dail, "I've been elected to lead but I promise to serve". His vision is to transform Ireland into a "republic of opportunity".
In his acceptance speech, Varadkar emphasised youthful energy, arguing that the politics of the past were no longer fit for goal.
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Ball then got the wish he and his father, LaVar, wanted all along by staying in Los Angeles, where he starred last season at UCLA. More than two dozen picks into Thursday night's National Basketball Association draft and not one senior has been selected.
As he made his acceptance speech, during which his parents watched from the visitors' gallery, he paid fulsome tribute to his immediate predecessor Enda Kenny.
Sinn Fein leader Gerry Adams congratulated Mr Varadkar and welcomed his family to Leinster House on "a proud day for them".
SDLP Leader Colum Eastwood MLA extended his congratulations to the new Taoiseach Leo Varadkar and called for the Irish Government to "reassert its role as co-guarantor of all our political agreements". "I wish him well", Mr Adams said.
It comes as he recently won the Fine Gael party leadership on 9th June 2017.
He said: "While it might be a milestone for me personally, in the context of the country that's irrelevant".
Labour Party leader Brendan Howlin paid a warm personal tribute to the new Taoiseach and wished him and his partner well.
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.
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