Ireland sought emergency help three years ago to keep its finances under control and has met the terms of the programme, cutting spending and raising taxes to bring down its budget deficit and rebalance the economy.
"This isn't the end of the road. This is a very significant milestone on the road," Noonan told a news conference. "But we must continue with the same types of policies."
José Manuel Barroso, the President of the European Commission, sent his congratulations to the Irish government and people. "Thanks to their efforts and sacrifices, Ireland will now be able to finance itself through its own efforts."
Barroso stressed the EU's role in helping to make the Irish programme a success. "Today's result would not have been possible without the solidarity and significant financial support of the other EU member states," he said in a statement.
"I am proud of the efforts and contribution of the European Commission. We have stood by Ireland throughout, including through our insistence on the lengthening of maturities and on the reduction of the interest rate," Barroso said.
The Irish finance ministry was also keen to celebrate the day on social media, using the hashtag #irlexit on Twitter.
No easy ride
But the bailout talks were no easy ride for Ireland, which faced intense pressure from EU countries to revise its super-low rate of corporate tax in exchange for the money.
Britain and Germany have long viewed low Irish taxes as a form of unfair competition and the finance ministers of Austria and France said the corporation tax may have to be raised as part of any deal.
Ireland stood strong, saying the tax rate was "non-negotiable".
More pressure then came from within. The bailout deal, signed in November 2010, fuelled a sense of national outrage at the handling of the economic crisis and the prospect of a draconian austerity programme for the next four years. Under pressure, the government coalition collapsed, forcing elections to be held.
The election campaign that ensued was fought on the basis that Ireland will renegoiate the terms of its €85 billion EU/IMF bailout. That battle was fought relentlessy by Micahel Noonan, the Irish finance minister, who managed to secure a better interest rate.
Three years on, economic growth is slowly returning to Europe and Portugal aims to follow Ireland in completing its bailout next year, but deep problems remain particularly in Greece, stuck deep in depression.
Ireland's economy is forecast to grow by about 2% next year, unemployment has fallen below 13%, from a 15.1% peak in 2012, and Dublin is confident enough to do without a backup credit line as insurance against market shocks.
The country of 4.6 million is funded into 2015 thanks to debt issuance over the last 18 months and is showing the way to Greece, Portugal and Cyprus - which have also had sovereign bailouts - and Spain, which has had help for its banking system.
But after the struggle to convince financial markets that Ireland's economy is back on track, Prime Minister Enda Kenny's government now has to win over the Irish people.
While pledging to maintain fiscal discipline, Noonan said he will consider income tax cuts in the next two budgets to give the economy some support.
"If we can make changes which help the economy to grow better and create extra jobs, those are the kind of things we'll do," he said.