More than 18,000 permits to work in the Republic were issued last year to citizens of 127 non-EU countries by the Department of Enterprise, Trade and Employment.
The figure is a three-fold increase on the number of permits issued in 1999 and it is forecast to increase to 25,000 this year.
The majority of permits went to Latvia, the Philippines, the US, Czech Republic and Poland but hundreds of permits were also granted to Lithuanians, Malaysians, Romanians, Russians, Brazilians, Canadians, Estonians and Indians.
Most of those who arrived here are working in the services and catering industry.
In addition, 1,387 working visas and work authorisations were issued. Citizens of some countries need visas as well as permits to work. Visas went mainly to highly skilled professionals working in the medical and IT sectors.
More than 2,000 work permits were issued to Latvians, who do not require a visa to travel here. In the Republic, they work mainly in the horticulture, retail and engineering sectors.
Mr Brendan Butler, director of social policy for the Irish Business and Employers' Confederation (IBEC), said it was clear employers were forced to go further afield to fill jobs.
"The number of Irish people available to come back from overseas is slowing down. Up to a year ago, half of those coming to work in Ireland were returning immigrants but at this stage most Irish people who want to come back or are in a position to come back have already done so," he said.
He said there were a number of "hiccups" during the year when "the system found it difficult to cope" with the number of applications for work permits.
At one stage it took up to eight weeks for applications to be processed, he said, but the Tanaiste, Ms Harney, had given a commitment to IBEC to get this down to one week. "That is absolutely vital."
Mr Patrick Maher, executive director of development for Enterprise Ireland, said a recent survey of businesses conducted by it found the burning issues for employers were staff shortages and staff retention. "These issues are miles ahead of e-business, the euro and globalisation, which one would expect employers to be exercised about," he said.