He said the country was at an important crossroads and it was important not to make the mistakes of the past.
"And also devolving a new social contract".
Local TD Peter Fitzpatrick has thrown his support behind Simon Coveney in the race to become the new Fine Gael leader.
Mr Donohoe stated his intention to vote for Mr Varadkar in an interview on RTÉ's Morning Ireland.
"He is the most substantial and capable politician of my generation", Mr Donohoe told Newstalk.
Enda Kenny - who had already announced he would not lead Fine Gael into the election - said on Wednesday he would remain prime minister during the contest, due to be concluded on June 2, and subsequent talks with government officials backing the government.
"I think history will judge him kindly as he led our country out of a very dark period to a position today where the economic revival is slowly spreading to the regions". It said 13 backed Coveney.
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But at a parliamentary election a year ago, Fine Gael suffered a backlash from voters who felt the recovery was passing them by.
Early on, potential candidates Frances Fitzgerald and Richard Bruton declared they would not be running, paving the way for Coveney and Varadkar to take centre stage.
Mr O'Donovan said he believed the Minister for Social Protection had the best attributes for the job.
"And open a conversation with people that don't support us, people who have lost faith in us or people who maybe never considered voting for Fine Gael but start that conversation with them". He is throwing his weight behind the Housing Minister.
The latter alludes to Varadkar's plain-speaking manner, which supporters say could widen the party's appeal. 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.
Votes by parliamentary party members (TDs, Senators and MEPs) have more weight than the other colleges.
Varadkar quietly launched a website yesterday asking for the public's help and said he is "looking forward to getting the campaign going around the country".