"History will judge Enda Kenny's reign favourably," said Philip O'Sullivan, an economist with Investec in Dublin. "While the execution was not always perfect, his Administration's willingness to take often unpopular decisions was a key ingredient in restoring the country's creditworthiness and turning the economy around."
Lauded abroad by bankers and investors, Kenny is regarded less favourably at home, and support for his coalition collapsed in last year's election. That forced him into a so-called rainbow alliance to keep power, and he pledged to step aside before the next election, due within five years.
Varadkar, the openly gay son of an Indian immigrant, has moved into the favourite's slot to become prime minister, Paddy Power Betfair odds show.
"While the Fine Gael leadership election will generate no shortage of media coverage, we struggle to identify meaningful policy differences between the two front-runners," said O'Sullivan. "Irrespective of who wins, we think 'business as usual' will be the real result."
The new leader will be chosen by early June, as talks on the UK's departure from the European Union near. While Ireland is considered to be the European economy most vulnerable to Brexit, the economy is in better shape to withstand such a shock than when Kenny took power from Brian Cowen in 2011.
Unemployment has fallen to about 6 per cent from a peak of 15 per cent in January 2012, borrowing costs have dropped below the UK's and Ireland has remained a favoured destination for US companies seeking a foothold in Europe.
JPMorgan Chase this month agreed to buy a new office building in Dublin, with room for more than 1000 workers, as it continues to plan for Brexit.
Kenny also won plaudits for his moves on social issues. In 2015, Irish voters backed a proposal to allow gay marriage by almost a 2-to-1 margin, making the nation the first in the world to back wedlock for same-sex couples in a referendum.
He also took on the Catholic hierarchy, saying in 2010 that the Vatican's handling of abuse scandals smacked of "elitism and narcissism," some of the sharpest language an Irish leader has ever used against the church.
At times, though, Kenny's tenure has been marked by missteps. Last year, the PM apologised for describing opponents as "whingers," and drew fire after saying that the "vast majority of people don't understand economic jargon".
Kenny's penchant for homespun wisdom can also grate. In 2015, he spoke of a "man who stopped me with two pints of beer in his hand" to complain about the introduction of water charges. "Two pints in one hand?" Sinn Fein leader Gerry Adams asked. "They must be some big hands, right?"
- Bloomberg