Simon Coveney managed to win the support of a majority of ordinary members
The new Fine Gael leader says the whole experience is still a "bit surreal".
Leo Varadkar secured 60% of the vote to Simon Coveney's 40% in the Fine Gael leadership contest.
The Social Protection Minister is likely to become Ireland's youngest Taoiseach later this month, after Fianna Fáil confirmed they intend to honour their confidence and supply agreement with Fine Gael - paving the way for the Dáil to confirm Leo Varadkar.
In his first press conference, Minister Varadkar said he would be open to keeping Independent Ministers in their roles, and refused to rule out a future coalition with Fianna Fáil.
The Dublin West TD and now Taoiseach-elect secured the public support of a majority of parliamentary party members, including Frances Fitzgerald, Richard Bruton and Charlie Flanagan.
70% of his parliamentary colleagues backed the new leader in the ballot, compared to 30% for Simon Coveney.
BREAK VARADKAR WINS PP 51-22 is Fine Gael leader and Taoiseach. Elect— Páraic Gallagher (@paraicgallagher) June 2, 2017
However, Minister Varadkar did not manage to win a majority of support from the party's ordinary members.
Simon Coveney picked up 65% of the vote from members, while Leo Varadkar only managed 35%. Members count for 25% of the electoral college.
The Social Protection Minister also won 55% of votes from Fine Gael councillors.
Mr Varadkar told reporters the win was still sinking in.
"I was thinking I might go to bed tonight, and wake up Minister of Transport, Tourism and Sport, and wonder did everything that happened in the last two years really happen," he said.
In his speech after the vote, Minister Varadkar said: "This contest has reminded many of us what inspired us to join Fine Gael."
Varadkar - who is openly gay, and whose father emigrated to Ireland from India - suggested his election has shown that "prejudice has no hold in this Republic".
He added: "I know when my father travelled 5,000 miles to build a new home in Ireland, I doubt he ever dreamed that his son would someday grow up to be its leader - and despite his differences, his son would be treated the same, and judged by his actions and character, not his origins and identity."
Minister Varadkar said that, if elected Taoiseach, he will "seek to serve this country with integrity, passion & determination, and courage."
Minister Coveney, meanwhile, conceded the election, saying: "[Varadkar] is a worthy leader of this contest, and he has the potential to be a hugely successful leader of this party that can broaden our horizons to new successes that we have not seen yet.
"I will work with him, side-by-side, to do everything I can to make sure that that happens."
Leo Varadkar (38) was first elected as a TD in 2007, and has also served terms as transport minister and health minister.
While Minister Varadkar will replace Enda Kenny as Fine Gael leader, Mr Kenny will remain as Taoiseach until he formally steps down and the Dáil votes to accept his successor.
That process is not likely to take place until at least June 13th, as the Dáil is not scheduled to sit next week.
In a statement after the result, the outgoing leader said: “I want to extend my heartiest congratulations to Leo Varadkar on his election as Leader of the Fine Gael party. This is a tremendous honour for him and I know he will devote his life to improving the lives of people across our country. He will have my full support in the work that lies ahead."
He thanked Simon Coveney for making the election "a real contest".
Mr Kenny added: “As I said when I stepped down as party leader, I will now provide a brief but appropriate period for Leo Varadkar to engage with groups and members supportive of Government, and with other Parties in the Dáil, regarding provision of Government for the future."
If confirmed by TDs, Minister Varadkar will become the youngest ever Taoiseach, and Ireland's first openly gay leader.
Confirmation of Leo Varadkar as Taoiseach seems likely after Fianna Fáil leader Micheál Martin confirmed his party is committed to maintaining their confidence & supply agreement with Fine Gael.
In a statement, he said: “I look forward to meeting with the new Leader of Fine Gael [...] I will be emphasising the need for renewed focus on executing and delivering the commitments in our three-year agreement.
“I will also be emphasising the need for the upcoming discussions on Budget 2018 to be open and transparent with no surprises."
Sinn Féin's Gerry Adams, meanwhile, called for an election following today's results.
Deputy Adams said: “I congratulate Leo Varadkar on his appointment as Fine Gael Leader. However, his elevation to the position of Taoiseach is another matter entirely.
“Leo Varadkar as Taoiseach will mean greater disadvantage. It will mean more people locked out of the housing market. It will mean the growth of precarious work and poverty wages. Ultimately, it will mean the widening of the gap between the rich and the poor."
People Before Profit's Richard Boyd Barrett criticised the new Fine Gael leader's proposals to restrict strikes for workers in some essential public services.
Deputy Boyd Barrett suggested that it illustrated “a very right-wing and anti-working class bias that would exacerbate social divisions and hamper the struggle for greater economic equality and fairness in Irish society".