The NTMA has swapped €3.53 billion worth of bonds due in 2014 for new bonds due for repayment in 2015.
The swap effectively refinances 30% of the bonds due for repayment in January 2014, immediately after the EU/IMF programme ends.
Today's auction is the first significant test of market sentiment toward Irish government debt since the bail-out deal in November 2010.
The new bonds were issued with a yield of 5.15%. Last July, Irish three year bonds hit a peak yield of 22.5%.
A National Treasury Management Agency spokesman said the agency was very pleased with the strong take-up of this switch offer.
''This exercise has demonstrated investor appetite for Irish government paper and will support our plans for a phased re-entry to long-term debt markets,'' he added.
"Today's exercise is a very positive surprise for an Irish bond market that has seen no NTMA involvement since September 2010,'' commented Donal O'Mahony, Global Strategist at Davy.
''It reflects the sustained improvement in market sentiment over the past two months, which has lowered bond yields of all maturities into the 5-7% zone from 9-10% previously'', he added.
Around €12 billion of government debt is due for repayment in 2014, the year after the EU/IMF funding programme ends. The bond swap exercise is aimed at moving some of that money into 2015 - when no government bonds are due to be repaid - in order to reduce the amount of funds that will have to be raised in 2014.
The NTMA has been encouraged by the sustained falls in the yield in Irish Government bonds, particularly short-term debt. Yesterday yields on Irish five-year bonds fell below 6%, compared with a yield of almost 18% last summer.
The yield on Irish 2014 bonds fell to 5.3% this morning when the news was announced. The yield on 10-year bonds was just under 7.5%.
The NTMA says this marks its first significant engagement with the bond market since September 2010.
"This offer is in response to approaches from market participants and will help address demand for Irish government paper maturing in 2015 that is currently unmet," the agency said.
"No choice" on Anglo payment - Noonan
The Tánaiste and the Minister for Finance have said that Ireland has no choice but to pay €1.25 billion to Anglo Irish Bank bondholders today, as not doing so would cost the country more.
Finance Minister Michael Noonan said earlier today that the ECB had told Ireland all along that the consequences would be serious if we did not pay.
Tánaiste Eamon Gilmore said he understood that taxpayers were annoyed at having to pay unsecured bondholders. He added that the Government was continuing to discuss Ireland's debt situation with the troika and he would be hopeful of a result.
Protests about the payment to bondholders are planned by anti-household tax activists and TDs at Anglo Irish Bank's former offices on St Stephen's Green in Dublin.