Leo Varadkar was elected Irish Prime Minister on Wednesday, making the 38-year-old son of an Indian immigrant the once-staunchly Catholic country's first gay premier and the youngest person to hold the office.

Despite inheriting Europe's fastest-growing economy, he will face immediate challenges in the shape of neighbouring Britain's exit from the European Union, a political crisis in Northern Ireland and a housing crisis at home.

Varadkar succeeded Enda Kenny earlier this month as leader of the governing Fine Gael party, with colleagues pinning their hopes of an unprecedented third term on the straight talking Varadkar, who they believe can widen their appeal in elections that may be triggered as soon as next year.

"Enda Kenny's leadership enabled me to become an equal citizen in my own country two short years ago and to aspire to hold this office, an aspiration I once thought was beyond my reach, at least if I chose to be myself," Varadkar said in reference to Ireland's 2015 vote to legalise gay marriage.

"The government I lead will not be one of left or right. The government I lead will be one of the new European centre as we seek to build a Republic of opportunity, that is a Republic in which every citizen gets a fair go and in which every part of the country stands to share in our prosperity."

Varadkar's elevation marks another chapter in the social change that has swept through the country of 4.6 million people that only decriminalised homosexuality in 1993 and legalised divorce two years later.

"As the country's youngest holder of this office, he speaks for a new generation of Irish women and Irish men, he represents a modern, diverse and inclusive Ireland and speaks for them like no other," Kenny told parliament, nominating his successor.

However it is his policies that will attract more scrutiny at home with opponents warning that the former health, tourism and social protection minister, who first joined the centre-right party aged 17, would nudge it further to the right.

While analysts expect few major policy shifts from Varadkar and his new cabinet, which he is due to name later on Wednesday, the new Fine Gael leader has hinted at some changes.

He has pledged to introduce a less ambitious debt reduction target than the one set by Kenny's government last year and lobby the European Union for additional leeway to free up more funding for badly needed infrastructure projects.

On Brexit, he wants Northern Ireland, a British province, to remain in the EU's single market and retain access to as many EU programmes as possible to ensure it secures a soft Brexit that he has said appears more likely following last week's British election.

Varadkar, who took his seat in parliament 10 years ago to the day on Wednesday, is expected to promote Public Expenditure Minister Paschal Donohoe later on Wednesday to finance minister, replacing the retiring Michael Noonan.