He added: "We are now at a crossroads as a country.
Whatever I do next it will be different, not politics", he said.
And he promised to reveal a series of policy papers over the coming days.
National broadcaster RTE said last week that of those in the parliamentary party who had confidentially declared their support - around half - 23 favored Varadkar, the son of an Indian immigrant who is Ireland's first openly gay minister.
Louth Deputy Peter Fitzpatrick, meanwhile, has announced he will vote for Simon Coveney.
The other is Simon Coveney, the housing minister, who is the son of former Fine Gael minister Hugh Coveney.
Enda Kenny will stay on as Taoiseach until that process concludes.
The two challengers were left to fight it out as Justice Minister Frances Fitzgerald and Education Minister Richard Bruton ruled themselves out of the race.
Speaking on RTÉ's Today's with Seán O'Rourke programme he said a leadership election is time for renewal and Mr Varadkar reflects a changing Ireland, a diverse Ireland and will broaden Fine Gael's support base.
He announced past year that he would not lead Fine Gael into another election but has delayed his resignation several times in recent weeks amid discussions about Brexit in Brussels.
Mr O'Donovan said he believed the Minister for Social Protection had the best attributes for the job.
Following Enda Kenny's resignation as party leader from midnight last night, the Westmeath Independent contacted a number of local Fine Gael representatives to ask whether they wanted Minister Coveney or Minister Varadkar to become the next Taoiseach.
Mr Kenny paid tribute to constituents and supporters in Mayo who he has represented since 1975.
Minister McHugh made no comment on the forthcoming leadership contest that is set to follow the announcement.
Fine Gael are planning to hold their Longford Fine Gael selection convention next month after Enda Kenny's successor as party leader is announced.
"And also says that people should have an equal opportunity in this society to succeed".
The Fine Gael leadership will be decided by an electoral college that gives the parliamentary party - TDs, Senators, and MEPs (Members of the European Parliament) - 65 percent of the vote.
He said he did not see any major failings with Minister Varadkar and his choice was more down to Minister Coveney's attributes and work in the past.