The decision not to seek a special overdraft facility was finalised at an emergency cabinet meeting today ahead of Finance Minister Michael Noonan flying out to a summit in Brussels.
Ireland will leave the bailout, overseen by Europe and the International Monetary Fund (IMF) since 2010, on December 15.
"This is the right decision for Ireland," the Taoiseach said.
"We will exit the bailout in a strong position. The Government has been preparing for a return to normal market trading.
"We will set out a path to a brighter economic future for our people, a path from mass unemployment to full employment from involuntary emigration to the return of thousands of people who have to leave for other countries to find work.
"Today is just the latest step in that ongoing journey, a significant step indeed but also just another step towards our ultimate job of getting Ireland working again."
The Department of Finance said the Government's assessment was that leaving the €85bn bailout without a so-called backstop of credit was the best option.
It said market and sovereign conditions are favourable towards Ireland. The country has built up more than €20bn in cash reserves since returning to the international money markets last year.
It said this can be used to keep Ireland in the black until early 2015.
It also said the latest Budget, announced last month, had been designed to deliver a primary balance or small surplus.
"Domestic and international economic conditions are improving, monetary policy decisions are conducive to exit and confidence and sentiment towards Ireland has improved considerably in recent months," the department said.
Mr Noonan was briefing Cabinet colleagues before setting off for Brussels where he is to meet European finance chiefs at the Ecofin meeting tomorrow.
He had indicated in the past that the Government would take this course.
Ireland's finances, budgets and policies have been overseen by a Troika of the IMF, the European Central Bank and European Commission since they agreed to the massive loan package in late 2010.
In an understated address to the Dáil confirming the end of the bailout, Mr Kenny warned that difficult days still lie ahead.
"Neither today's decision, nor the exit from the bailout in December, means the end of difficult economic decisions. There are still demanding times ahead," he said.
"It does not mean any windfall of cash. It won't mean that our economic and financial challenges are over."
Mr Kenny said the Government is to publish a medium term economic strategy - a plan based on enterprise and not the speculation that led to the country's collapse five years ago.
"Never again will our country's fortunes be sacrificed to speculation, greed and short-term gain," he said.
Despite a cautious tone in the announcement, the opposition accused the Government of "bravado".
Fianna Fáil leader Micheal Martin, who served as a Minister in the previous coalition government that had to bring in the international bailout, said a precautionary credit line would have served as security.
"It's not a sign of weakness, it's a sign of security - and maximum security for this state," Mr Martin said.
"It's not that you might crash into somebody, but somebody might crash into you. It's fundamentally an insurance policy for the people of this country."
His assertion that the Government should have consulted the Dáil on the bailout decision provoked a loud and angry reaction from Government Deputies, particularly Pat Rabbitte.
The Troika aren't gone. They will continue to control budgets & require us to inflict massive further cuts to pay off 200 billion of debt— Richard Boyd Barrett (@RBoydBarrett) November 14, 2013
While applauding the fundamental decision, Sinn Féin leader Gerry Adams criticised the Government, saying: "The Troika may be leaving, but the Troika mindset remains.
"Your Government has introduced many austerity measures that were not recommended by the Troika.
"You have taxed and cut the most vulnerable in Irish society, unbidden by your European masters.
"Next year, whether the Troika is here or not, you will take €2bn more from the economy in water charges, taxes and more cuts to health, education and other vital services."
FF blame FG/Lab for implementing FF policy. FG shouting down FF while implementing FF policy. Tweedledum and Tweedledee.— Thomas Pringle T.D. (@ThomasPringleTD) November 14, 2013
Ireland has been given assurances by its European and international partners that they will continue to offer their full support to the country.
The Taoiseach said German chancellor Angela Merkel pledged to work closely with Ireland to improve funding mechanisms for the economy, including access to finance for small and medium businesses.
"The German government has asked KFW, the German development bank, to work with the German and Irish authorities swiftly, in order to deliver on this initiative at the earliest possible date," Mr Kenny said.