Leo Varadkar has praised Theresa May as an "honourable and deeply passionate politician who did her best for her country".
The Taoiseach said he and the outgoing prime minister had got to know each other very well in the past two years.
"She is principled, honourable and deeply passionate about doing her best for her country and her party," he said.
"Politicians throughout the EU have admired her tenacity, her courage and her determination during what has been a difficult and challenging time.
"Theresa May strove to chart a new future for the United Kingdom. I want to wish her the very best for the future."
However, Mr Varadkar warned that British politics was entering a phase that could be "very dangerous" for Ireland.
He said a Eurosceptic Tory who wants to "repudiate" Britain's EU Withdrawal Agreement could replace Mrs May.
Mr Varadkar said no matter who replaced her, Ireland would hold its nerve.
Speaking after voting in the European and local elections, he said: "British politics is consumed by Brexit and will be consumed by Brexit for a very long time.
"It now means we enter a new phase when it comes to Brexit and a phase that may be a very dangerous one for Ireland.
"Whatever happens, we are going to hold our nerve, we are going to continue to build and strengthen and deepen our alliance across the European Union, and we will make sure we see Ireland through this."
He said of Mrs May: "We worked closely on issues over the past one-and-a-half years on Brexit and the North. I particularly want to pay tribute to her to agreeing to retain and strengthen the Common Travel Area.
"As a result, British and Irish citizens are able to live, work, study, travel and access health care, housing, education and welfare and pensions in each other's countries as though we are citizens of both.
"That is going to be there and protected, no matter what else may happen."