Ireland's Leo Varadkar on Saturday took over as premier for the second time in a handover of power in line with a coalition deal struck in 2020.

Varadkar replaced Micheal Martin as Taoiseach (premier) in a rotation between his Fine Gael and Martin's Fianna Fail parties that is unprecedented in Irish history.

The centre-right parties, the two main political partners in a three-party governing coalition, were forged from opposing sides in the Irish Civil War in the early 20th century.

They agreed to the rotating premiership as part of a coalition with Ireland's Greens following 2020 elections.

Varadkar, who is mixed race and openly gay, is stepping up from deputy premier.

At 43, he is still one of Ireland's youngest ever leaders, even in his second stint in the role.

Speaking at a special sitting of the Irish parliament in Dublin, Varadkar paid tribute to his predecessor Martin who had provided "reassurance and hope in difficult times".

"I accept this nomination with humility and resolve and a burning desire... to provide new hope and new opportunities for all our citizens," he said.

In a video posted on social media, Martin earlier said it had been "the honour of a lifetime to serve" as Taoiseach.

Varadkar's rise to the top of Irish politics was remarkable in a country dominated by a strict, conservative Catholic morality well into the latter half of the last century.

He became the country's youngest Taoiseach at the age of 38 as well as its first openly gay head of government and first of Indian heritage.

Varadkar was born in Dublin to an Irish mother who worked as a nurse and an Indian immigrant father, who was a qualified doctor.

After gaining a medical degree from Trinity College Dublin, he went into general practice but stayed involved in politics, and in 2007 secured election for Fine Gael in Dublin West.

In 2015, before Ireland's referendum legalising same-sex marriage, Varadkar came out publicly as gay. 

His tenure as Taoiseach, however, was overshadowed by Brexit and the pandemic during which he re-registered as a doctor and returned to work once a week while continuing to lead the country.