Ireland was the only EU member state to hold a referendum on Lisbon, though there have been calls for referendums in several countries.
"The Irish people have spoken with a clear and resounding voice," Mr Cowen said in a brief statement to reporters. "It is a good day for Ireland and a good day for Europe.
"The Irish people showed an Ireland embracing her future with Europe," he said.
The Irish anti-Lisbon group Coir said on Saturday: "We are extremely disappointed that the voice of the people was not heard the first time around."
EU hails 'victory'
Swedish Foreign Minister Carl Bildt, whose country currently holds the EU presidency, called the vote "an important victory for Ireland and for all of Europe".
He said it was just a matter of time until the EU "finally can push the button for the better European co-operation that the Lisbon Treaty will give us".
Brian Cowen: "The Irish have supported reforms so the EU can become more efficient and more effective"
Irish opinion is thought to have swung behind the "Yes" vote this time because of the severity of the economic downturn, as well as the legal "guarantees" on Irish sovereignty that the EU pledged after the first referendum.
The legally binding "guarantees" state that Lisbon will not affect key areas of Irish sovereignty, such as taxation, military neutrality and family matters such as abortion - significant issues in last year's campaign in Ireland. But they have not yet been attached to the treaty.
The treaty is intended to make EU institutions better suited to the enlarged bloc of 27.
Declan Ganley: "Politically a masterful campaign"
But opponents see it as part of a federalist agenda that threatens national sovereignty.
In last year's vote, 46.6% of Irish voted "Yes" and 53.4% "No", and the rejection of the treaty plunged the EU into political gridlock.
All of the republic's major parties campaigned for a "Yes" vote except the nationalist Sinn Fein. The party believes rejecting the treaty would mean a more democratic EU.
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