Varadkar was elected on Friday as leader of Ireland’s Fine Gael, the country’s biggest political party.
Varadkar secured 60 per cent of the total weighted vote in the contest while his only rival Simon Coveney, minister for housing, planning, community and local government, only took 40 per cent.
In mid May, Kenny retired as leader of Fine Gael under pressure from both inside and outside of the party.
In a statement after Varadkar’s victory, Kenny congratulated his successor as leader of Fine Gael, saying that he wanted to extend his “heartiest” congratulations to Varadkar.
“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,” Kenny said.
The current taoiseach said he will now provide a “brief but appropriate” period for Varadkar to form a new government.
“The most important priority has to be the continued progress of our country led by Fine Gael in government. I know that Leo has the capacity to provide the leadership required in order to achieve this,” Kenny said.
Varadkar, while delivering his victory speech, said he was honoured to be elected as party leader.
He said it is the start of a more democratic, more engaged and more inclusive Fine Gael party.
Earlier, his only rival Coveney pledged full support to the new party leader. Coveney said Varadkar was a worthy winner of the contest and that he would work side by side with him to do everything he could to help the new leader.
Born on January 18, 1979 in Dublin, Varadkar is the youngest child and only son of an Indian immigrant father and an Irish mother.
The young Dubliner was 22 when he entered Irish politics. At 27, he was elected to parliament.
Varadkar will become the youngest taoiseach in the history of the country at 38.
The Dail Eireann, the lower house of the Irish parliament, must now vote to ratify Varadkar, a move that is expected to take place within the next fortnight.