Ireland's prime minister, Enda Kenny, who helped steer the country out of recession following the global financial crash, has announced that he is stepping down as the leader of his Fine Gael party.
Mr Varadkar said it had been his idea originally to extend voting rights for the leadership of Fine Gael to all the party's elected representatives.
"I want to lead a party and a country that can heal numerous divisions that have opened up over the last decade or so".
Minister for Social Protection Mr Varadkar was speaking at a press event at Dublin alongside the Minister for Public Expenditure Paschal Donohoe, who publicly endorsing him earlier today.
He is the first Fine Gael leader to win re-election to office.
Under Fine Gael rules this timeline would facilitate a two-and-a-half week contest, with voting taking place over the bank holiday weekend.
Minister Noonan said that he would continue to carry out his duties until a new party leader is elected.
He said that like any politicians, Mr Kenny had "his highs and lows" but he praised general his performance over two governments.
"Having inherited a country and an economy that was decimated by mismanagement, Enda's strong leadership and ability to make hard decisions was recognised both at home and overseas and saw our global reputation restored and strengthened", Mr Heydon said. One that says to people that if you contribute to the system, the system is there to support you.
Mr Varadkar, a doctor from Dublin and the favourite for the job, is Ireland's first openly gay member of cabinet.
"He understands, as he said last week, the unique circumstances of Donegal, cut off from the rest of the North for most of the last century by partition, and cut off geographically and in other ways from the rest of the State".
If the two parties can not agree, it would trigger national elections and Kenny would stay in office as head of a caretaker government.
Meanwhile the Irish finance minister Michael Noonan has announced he is set to retire from politics at the next election.
The current housing minister has also been in charge of several portfolios including agriculture and defense.