Investors have committed a total of €5.23 billion into longer-dated bonds maturing in 2017 and 2020.
The NTMA says of this, some €4.19 billion was new money for the purchase of the two longer-term bonds on offer - a new 5 year bond maturing in October 2017 and an existing bond maturing in October 2020.
A further €1.04 billion was for the exchange of their holdings of the shorter-dated 2013 and 2014 bonds into the 2017 and 2020 bonds.
The 2017 bond carried a yield of 5.9% and the 2020 bond a yield of 6.1%. The weighted-average yield on the combined transaction was 5.95%.
Speaking today, NTMA Chief Executive John Corrigan said: "We are very pleased with the success of today's transaction, particularly the fact that investors committed more than €4 billion of new money to our first long-term issuance since September 2010.
"This marks a very significant step for Ireland on the way to full bond market access. As a result of today's transaction, the NTMA has now covered a significant proportion of the €8.2 billion bond maturing in January 2014 which up until now has been seen as a challenging "funding cliff," he added.
It marked Ireland's re-entry to the primary market with longer term bonds for the first time since the EU/IMF bailout in 2010.
The Minister for Finance Michael Noonan has said the vast bulk of investors in today's bond sale are from overseas.
Speaking on Six One news this evening, he said "quite a good chuck of the money came from the US" but there was some investment from Europe too.
He said Ireland is now back in the market for the long-term and today was a very significant step in building confidence in Ireland.
Minister Noonan said the serious discussions on December's budget have not got underway yet but he said what happened today will not have any impact on them.
The Secretary General of the Department of Finance has described today as a very good day for the Irish economy.
John Moran said that "what we wanted to gauge was not just how much people would roll over their positions but would actually want to come back in, which is really selling to new investors."
He also said the figure of €4.19 billion was a very satisfactory result.