"I think Apple are here for the long term – many of the others are intent on expanding and not contracting. That's because of the range of technology, our track record and essentially our talent pool which is quite extraordinary given the flexibility of our education system," he told CNBC, speaking from Europe's largest annual start-up and technology event, the Web Summit.
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"Ireland is not afraid, we are pioneers again in a leading position," he added.
Ireland is set to close the "double Irish" loophole -- which allows companies to channel royalty payments for intellectual property from one Irish subsidiary company to another that is based in a tax haven -- from the beginning of next year, following pressure from the European Union.
From January next year companies setting up in Ireland will no longer benefit from the structure.
Other beneficiaries of the Double Irish include Facebook and Yahoo and some of the world's largest pharmaceutical companies.
The Irish government announced plans to close the loophole in its budget last month after the European Commission threatened to launch an investigation into the structure.
Existing companies will have a transition period until 2020 and Kenny said the development of an information "patent box" or corporate tax subsidy arrangement is in the pipeline.
"The development of our our information patent box will make Ireland really a global hub for innovation an entrepreneurship," Kenny said.
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"We haven't finalized the details yet, obviously we to be competitive in terms of the rates that apply. We would expect that when our information patent box is developed it will more than compete with any others and it will be perfectly legitimate in terms of our international obligations," he added.