He is also Ireland's youngest ever leader, at 38.
Ms Madigan said Mr Varadkar was "honest, genuine, with a first-class intellect".
Minister Coveney will move from Housing to Foreign Affairs and thus be responsible for Brexit negotiations.
These rightward-leaning economic stances stand in contrast with Varadkar's generally liberal positions on abortion rights and other social issues - and they drew criticism from Varadkar's rival for his party's leadership, Simon Coveney.
Walt Disney Company (The) (DIS) Receives "Overweight" Rating from Morgan Stanley
The investment managers in our partner's database now have: 928.49 million shares, up from 880.26 million shares in 2016Q3. Heathbridge Capital Management Ltd invested in 5.84% or 237,475 shares. 22,500 were accumulated by Navellier & Assoc Inc.
"This has never been about me.it has always been about the problems and challenges that the people of our country face", he said.
One of the first world leaders Varadkar planned to call after being appointed was British PM Theresa May.
In his first speech as Taoiseach, Varadkar told the Dail, the Irish Parliament, "The U.K. has been through some bad tragedies over the past few weeks so we offer them our sympathy and solidarity".
Although the dust has barely settled on a leadership campaign that only looked like providing one outright victor, the task of turning around Ireland's deepest problems is still on the horizon for Varadkar and his latest decision to move a number of key ministers to different departments could make or break his future as Dail Eireann's top dog.
Arriva North trains set for three-day strike in July
This is because of the on-going dispute over the "safety impact of the extension of driver-only operation and the removal of guards from services".
Varadkar was born in Dublin on January 18, 1979. "But all relatives shall gather at our home this evening", cousin Shubhada Varadkar told IANS on Wednesday morning.
"We also look forward to welcoming him on campus as Taoiseach and for staff and students to meet with him", he added.
Mr Kenny resigned as Fine Gael leader in May to make way for his successor.
"The new Taoiseach enters into office when our country is experiencing some of its greatest challenges since the formation of the state".
Emmanuel Macron's justice, defence and Europe ministers resign to defend sleaze allegations
When Bayrou threw his weight behind Macron's fledging party, the future president hailed it as a "turning point" in his campaign. Mr Macron had planned to rearrange the government after his centrist party won a majority in parliamentary elections on Sunday.
Naomi Long said: "Northern Ireland and the Republic have a good relationship and I am confident it will continue under his stewardship. We will be focused on the solutions of the 21st century and the future."...
- In video, girl begs mother for quiet after Castile shooting
- SuperValu Inc. (NYSE:SVU) Broker Price Targets For The Coming Week
- Wall St at record highs as tech stocks bounce back
- Ronaldo set to settle Spanish tax bill
- Britain's Prince Philip hospitalised with infection
- Novartis AG Common Stock (NVS) Reached a 52-Week High
- Vegas chooses Tomas Nosek in expansion draft
- Senate Health Bill: Cut Medicaid, End Penalties
- ACG orders 20 Boeing 737 MAX 10 jets
- California Judge Tosses Most Charges Against CMP Journalists Over Exposing Planned Parenthood