It is the second major jobs announcement this week, following on from the 900 new jobs at Kerry Group's facility in Naas in Kildare.
Mr Kenny said the Paddy Power announcement was a "statement of confidence by Paddy Power both in Ireland, in its people and in particular in our young people".
"It's an indigenous Irish company that has grown to have a global reach," he added.
The 600 jobs in Paddy Power's new headquarters in Clonskeagh in South Dublin cover highly-skilled areas such as e-commerce, technology and online marketing.
Paddy Power employs 2,172 people here already and it is due to fill all the 900 new jobs by 2015.
In a speech to some of the 1,000-strong workforce based in the Clonskeagh headquarters, the Taoiseach stressed the importance of maintaining Ireland's corporation tax rate of 12.5pc.
"Investors looking at Ireland have clarity, have a horizon against which they can plan and they understand that's not changing. And that creates certainty," he said.
"This is great news for Dublin South, for graduates and for Ireland.
It's a vote of confidence in Ireland's future and a boost for national self-confidence," she said.
Later today the Taoiseach is meeting with the Croke Park implementation body. "I propose to give the implementation body the evidence of what we believe can be squeezed from Croke Park in order to maximise savings,"