"I will retire as leader of Fine Gael effective from midnight tonight", Kenny said, opening the way for a swift leadership contest.
The governing centre-right party's new leader will be in place by the end of 2 June, Kenny said.
Earlier on Friday Fine Gael leadership challenger Simon Coveney admitted that the momentum is with Mr Varadkar but rejected any suggestion of conceding.
In a statement announcing his retirement, he said it had been a "huge honour and privilege" to lead the party over the course of 15 years.
MICHAEL Noonan is to step down as Minister for Finance and will not seek a seat in the next General Election nor will he seek a seat at the next cabinet table.
He said Minister Simon Coveney is "a very fine politician" but said he believes Mr Varadkar has the "rare combination of intellect and judgement needed for leadership".
Her predecessor David Cameron said Mr Kenny "was a strong leader for Ireland, a great partner for the United Kingdom, and remains a good friend".
The Mayo TD, first elected to the Dáil in 1975, confirmed his departure at a meeting of the parliamentary party this evening. I have chose to implement that decision from today.
He added that he will "continue to carry out my duties and responsibilities as taoiseach" until his replacement.
Helen McEntee, another junior minister in Mr Varadkar's camp, said: "Look at the fresh new approach he has taken to politics, look at how he interacts with people, look at his vision for a more forward-thinking and open Ireland".
Taoiseach Enda Kenny is in London today for a number of engagements including a speech to the Ireland Funds Great Britain group.
So, scroll back up and vote for who you would pick as the next Fine Gael leader and likely taoiseach. "One of the fundamental tenets of our democracy is a commitment to public service and the Taoiseach [PM] has more than fulfilled that obligation".
Fine Gael chief whip Regina Doherty has publicly declared her support for Leo Varadkar as the party's next leader.
Around 21,000 Fine Gael members will be entitled to vote with TDs and Senators accounting for 65 per cent of the vote, delegates 25 per cent and local councillors the remaining ten per cent share.
Merkel said that Germany needs France to succeed, emphasising that "Europe will only do well if there is a strong France". She is scheduled to give a television interview on Thursday night and an announcement is expected by week's end.
Hemenway Trust Co LLC acquired a new position in shares of salesforce.com, inc. during the fourth quarter worth about $137,000. Wall Street analysts polled by Thomson Reuters have a current recommendation of 1.80 on a consensus basis for the stock.
Former friends Katy and Taylor are thought to have fallen out in 2012 when Katy dated Taylor's ex-boyfriend, singer John Mayer. Rose then said that she is simply doing what she always does and ended things with one final dig at Perry's music.
Headlined by Billboard , a publication giant in the world of music, these annual honours have been airing since 1989. If you don't have a TV login, you can still live stream the Billboard Music Awards - even for free.
Chicago went ahead to stay with five runs in the second against Scott Feldman (2-4), who was chased in the third. The benches cleared briefly after the top of the third when Cueto and Grandal exchanged words.
The contouring trend is still going strong, as demonstrated by influential models of the moment Bella Hadid and Emily Ratajkowski. Her pale satin gown by Twinset was designed with spaghetti straps and thigh-high split, according to Vanity Fair .
Moon has previously expressed ambivalence over the THAAD system and told Xi he was "well aware" of Chinese concerns about it. Moon also raised the issue of apparent economic retaliation against South Korean firms in China , he said.
The settlement - by Toyota , BMW, Subaru and Mazda - covers 15.8 million vehicles equipped with rupture-prone air bag inflators. District Court for the Southern District of Florida but that seems likely now that a settlement has been reached.
John McCain (R-Ariz.) said the president's mounting scandals were inching towards Watergate proportions. For the sake of the republic-as much today as in 1974-the president must be impeached.
Colorado man to be freed early now in immigration custody
Lima-Marin was a Cuban immigrant who came to the United States with his parents as a toddler during the 1980 Mariel boatlift. He said, 'Did you hear?' And I was like, 'Yeah, ' and I could just hear his smile", said Jasmine Lima-Marin.
IS fighters attack government-held areas in central Syria
The SOHR said at least 27 government troops or militia were killed in the attack, on the villages of Aqareb and al-Mabujeh. In recent months, the extremist group has suffered military setbacks and lost territory in the country.
Japan's cabinet approves Emperor Akihito abdication bill
Tokoro noted that before the current law was put in place in 1947, Japan had eight female emperors - who "did wonderful jobs". Only males can inherit the throne and there was a succession crisis until 2006 as both the emperor's sons had only daughters.
Average US 30-year mortgage rate slips to 4.02 percent
As a result, many prospective homebuyers who can not come up with a 20 percent down payment are unable to get a loan. Other key rates also fell marginally. 3 year ARM loans have been quoted at 3.000% and the April is 3.744%.
Indonesian soldiers killed in South China Sea exercise
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Singapore Airlines reports net loss in fourth quarter
The soft global cargo market helped push yield down 10.7 percent though, contributing to a revenue decline of SGD$89 million. SIA said this was affected by a 3.8 per cent contraction in passenger yield and a 1.4 per cent decline in passenger traffic.
Tom Hardy to star as Spider-Man villain Venom in solo film
Sony Pictures has started announcing the cast of Sony's Marvel Universe film " Venom ", which is set to release in 2018. Topher Grace played the character in Spider-Man 3 against Tobey Maguire, but less said about that, the better.
McGregor terms set; talks shift to Mayweather
The documents needed for McGregor to receive his license are related to medical exams and physical requirements. Both McGregor and Mayweather have openly courted the match-up in the media in recent months.
Three things to watch on Donald Trump's foreign trip
And in Sicily, the president will meet with the other leaders of the G7, a gathering of Western economic powers. In Israel, Trump will meet with Prime Minister Benjamin Netanyahu , looking to smooth over fresh tensions.
Lawmakers demand swift action for Turkish Embassy violence
The US President had promised to strengthen strained ties despite Erdogan's objections to the US arming of Kurdish fighters. Washington [U.S.], May 17: Nine protesters were injured outside the residence of the Turkish Ambassador here on Tuesday.