Update 10.45pm: New Fine Gael leader Leo Varadkar has denied there is a split in the party following the leadership campaign.
Ordinary members of the party voted heavily in favour of Simon Coveney, while Mr Varadkar won the majority of elected members' votes.
In his acceptance speech Leo Varadkar said he wanted to make Ireland a 'Republic of Opportunity'.
He also said the party will come together after two weeks of robust debate.
He said: "I don't think there's a split, there's a difference of opinion among the elected members and the ordinary members.
"But needless to say there were elected members who didn't vote for me and ordinary members who didn't vote for Simon Coveney. But what's always going to be the case in a political party, and it's definitely going to be the case for Fine Gael, is that people will accept the outcome.
"The overall outcome was clear, it was 60/40, it's been accepted already by Minister Coveney in a very gracious way when he spoke earlier, and I've no doubt that the party will come behind me as leader."
Update 8.44pm: The new Fine Gael leader says the whole experience is still a bit surreal.
Leo Varadkar beat Simon Coveney to the leadership of Fine Gael with a margin of 60%-40%.
In his first press conference Mr Varadkar said he would be open to keeping Independent Ministers in their roles, and refused to rule out a future coalition with Fianna Fáil.
He is likely to become Ireland's youngest Taoiseach later this month.
Mr Varadkar told reporters the win was still sinking in.
He said: "It's still a bit surreal to be honest, still a bit sinking in. I was thinking I might go to bed tonight and wake up as Minister for Transport, Tourism and Sport and wonder did everything that happened in the past two years really happen.
"But what I did say in my speech though, and I do really mean it, Ireland is a wonderful country and it is the kind of country that if people are given the opportunity to succeed, they can succeed."
Minister Coveney, meanwhile, said: "He 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."
Update 7.17pm: Leo Varadkar has said his election to Fine Gael leader proves that "every proud parent in Ireland today can dream big dreams for their children", writes Elaine Loughlin.
Speaking after securing an overall vote of 60% in the leadership contest this evening Mr Varadkar said: "I think if my election as leader of Fine Gael today shows anything it is that prejudice has no hold in this Republic."
He thanked his rival Simon Coveney and out-going Taoiseach Enda Kenny before turning to his own story.
To a packed Mansion House, Mr Varadkar said: "My father travelled 5,000 miles to build a new home in Ireland, I doubt he ever thought his son would one day grow up to become its leader.
"Despite the differences, his son would be treated the same and judged by his actions and character and not his origins or identity.
"And so every proud parent in Ireland today can dream big dreams for their children, every boy and girl can know that there is no limits to their ambition to their possibilities if they are given the opportunity.
"So let that be our mission as Fine Gael, to build an Ireland, a Republic of opportunity, one in which every individual is given the opportunity to meet their full potential and every part of the country is given the opportunity to share in our prosperity," he told a cheering crowd of Fine Gael members.
Update 6.45pm: Leo Varadkar has won Fine Gael's leadership contest and is now set to become Ireland's new Taoiseach on June 13, write Fiachra Ó Cionnaith and Elaine Loughlin.
The result was confirmed at Dublin's Mansion House on Friday evening despite a groundswell of grassroots support for rival Simon Coveney.
Mr Varadkar won the race to replace Enda Kenny primarily by dominating the parliamentary party vote and gaining 51 of the 73 available votes compared to Mr Coveney's 22 - a 60-40% split.
However, among grassroots members the result was flipped, with Mr Coveney gaining 65.1% of support from just over 10,000 members who voted compared to Mr Varadkar's 34.9%.
With Mr Varadkar narrowly winning the council section of the vote by 55% to 45%, this means there is a marked difference between who the members voted for and who politicians supported.
However, the party weighting system means Mr Varadkar has won as the parliamentary party represents 65% of votes, membership 25% and councils 10%.
Both candidates embraced amid a sea of reporters and supporters when the result was announced, before each speaking from the podium to the crowd.
Both Mr Varadkar and Mr Coveney stressed the party is united and that both candidates respect each others' views, with Mr Varadkar - the son of an Indian father and Irish mother - now set to become Ireland's youngest ever and first openly gay Taoiseach on June 13.
Update 6.35pm: Simon Coveney has paid tribute to Fine Gael's new leader, Leo Varadkar.
"This has been a fantastic process and experience for this party," Coveney said, adding it gave the party "an opportunity to look in the mirror."
Coveney expressed his support for the party's new leader.
"Together we are going to build upon the leadership of Leo Varadkar," he said.
Update 6.25pm: Leo Varadkar will become the next leader of Fine Gael.
Leo Varadkar received 60% of the electoral college votes and will become the 11th leader of the party.
He won 51 of 73 votes from TDs, Senators and MEPs voted for Leo Varadkar, while Coveney received the other 22 votes.
Results of votes cast by the Parliamentary Party. #FGLE17June 2, 2017
Results of the combined votes cast by the Electoral College. #FGLE17June 2, 2017
Update 6.10pm: Voting from the local representatives has been counted in the Fine Gael leadership election.
The results show 100 members voted for Simon Coveney, while 123 votes were cast for Leo Varadkar.
Results of votes cast by Local Public Reps. #FGLE17June 2, 2017
Votes from the third and final division, the parliamentary party, are now being counted and the results will be announced soon.
Update 6pm: Fine Gael leadership contender Simon Coveney has won two thirds of the grassroots membership vote, highlighting the divided nature of the party, write Fiachra Ó Cionnaith and Elaine Loughlin.
In the first of three announcements to be made this evening at Dublin's Mansion House, Fine Gael confirmed that out of a total valid poll of 10,823 - just over 50% of members - Mr Coveney won 7,051 and Leo Varadkar 3,772.
In percentage terms this means the Housing Minister is backed by 65.1% of grassroots party members who voted, with the Social Protection Minister supported by 34.9%.
Despite the two-to-one backing at grassroots level for Mr Coveney, Mr Varadkar is still expected to win the leadership contest.
This is because the membership electoral college accounts for 25% of votes in the race; the council electoral college 10%; and the parliamentary party of TDs, senators and MEPs 65%.
While the council section - which is now being counted - is predicted to be split 50:50 between the candidates, Mr Varadkar has a substantial lead among parliamentary party colleagues.
However, the grassroots result means that even if Mr Varadkar wins the historic vote, he will be taking charge of what is in effect a party divided between what its membership and politicians want.
Speaking to reporters moments before the first of the three electoral college results, Mr Coveney said he was "feeling pretty good" and that the 16 day leadership contest has "energised" the party.
Asked for his prediction of what will happen, he added: "I'd rather get an actual result first."
Update 5.50pm: The votes from the first division party membership, totalling 10,842, revealed 7,051 members voted for Simon Coveney, while 3,772 opted for Leo Varadkar.
The members votes account for 25% of the total in the electoral college system.
The councillors votes are worth 10% and 73 TDs, Senators and MEPs votes have a value of 65%.
The further counts will be announced later.
Update 4pm: Leo Varadkar is set to be elected the new leader of Fine Gael, despite a majority of the party's ordinary members appearing to vote against him.
Partial tallies from the grassroots voters suggest Varadkar has won only 32% of their votes, with Simon Coveney on 68%
The votes of TDs and Senators are worth nearly 400 times more and Varadkar is set to win nearly two-thirds of those.
Varadkar supporter Alan Farrell says the events will not undermine the significance of a Varadkar victory.
"Ultimately winning is winning, whether you win by one vote or whether you win by 5,000 votes. Winning is winning," he said.
"Whomever comes out on top in this particular competition will know that they engaged with everybody, right from the parliamentary party down to the branch secretaries up and down the country. I think that has been a really good experience for all members of Fine Gael."
Update 3.30pm: Counting is underway in the Fine Gael leadership race.
Leo Varadkar is widely expected to win if all those in the parliamentary party, whose votes hold more weight, vote for him, while Simon Coveney has more support among grassroots voters.
At Bloom in the Phoenix Park, Coveney was asked if he had managed to convince some declared Leo voters to switch sides.
"Well let's wait and see, we might surprise a few people later on," he said.
Coveney said he will accept the results of the voting, whatever that may be.
"Of course I'll support Leo. Leo's a good guy, we'll be a very good leader if he wins.
"Nearly 12,000 members have voted, 232 councillors have voted, 73 Oireachtas members have voted, and I'll respect the outcome. If I won I think Leo will respect the outcome too."
Update 2pm: Counting is beginning in the Fine Gael leadership election.
Around 11,500 votes are being counted at the Mansion House in Dublin.
Simon Coveney's hopes of overtaking Leo Varadkar depend on at least half a dozen of Varadkar's Dáil supporters switching sides.
"Anybody that gets involved in politics is not going to get involved in a small bit of ground hurling," said Sports Minister Patrick O'Donovan (pictured below).
"Politics is a bit like Clare and Limerick, a Sunday, and I want to wish Limerick the best of luck. There's always going to be a bit of skelping but that's a good thing.
"Ultimately at the end of the day, once the flesh wounds aren't too deep and people can like them and get on with it on Monday that's the most important thing from my point of view."
Update 12.28pm: Voting has closed in the Fine Gael leadership election.
Senators, MEPs and TDs have all had their say this morning in the race to replace Enda Kenny.
Leo Varadkar is the predicted favourite among parliamentary party members, who make up 65% of the vote.
While Simon Coveney has been more popular with the general public.
MEP Brian Hayes has been backing Varadkar to win, but he says the election won't divide the party.
"We'll have to just wait and see, but it's been a terrific campaign," he said.
Votes will be counted from 2pm, with a winner expected to be confirmed by 6pm.
Earlier: The result of the Fine Gael leadership race will be announced later, after TDs, Senators and MEPs cast their ballots.
Leo Varadkar is widely expected to emerge victorious and will replace Enda Kenny the week after next.
Last night the last of the ballot boxes for members and councillors around the country closed after four days of voting.
It is estimated that more than 10,000 of the 21,000 eligible to vote cast a blot.
This morning at 8am voting for the 73 TDs, Senators and MEPs opens until midday.
This afternoon counting will begin with the members votes counted first, they account for 25% of the total in the electoral college system.
The councillors votes which are worth 10% will then be counted and declared.
And finally those 73 votes which have a value of 65% will be counted and the new leader will be announced around teatime.
Leo Varadkar has had a clear lead from the start of this race, and despite attempts by Simon Coveney to get some to defect it does not appear that he has been too successful, but one never knows what the secrecy of the ballot could throw up.
1/5 - I remember this day almost 15 years ago & the sense of excitement & possibility.— Enda Kenny (@EndaKennyTD) June 2, 2017
3/5 Their participation in this internal election has been democratically valuable & has energised the @FineGael party across Ireland.— Enda Kenny (@EndaKennyTD) June 2, 2017
4/5 - I pledge my full support to whoever is elected, in the important work at Govt level, to which the new leader will have to dedicate...— Enda Kenny (@EndaKennyTD) June 2, 2017
5/5 ..their life in service of the people of this great Republic. My enduring belief in the potential of this country is boundless.— Enda Kenny (@EndaKennyTD) June 2, 2017