Rents are increasing at 11.9 per cent year-on-year, according to a report by property website Daft.ie.
Daft.ie said this was the highest rate of growth recorded since its Rental Index started in January 2002.
The average rent nationwide now stands at just under €1,400 - almost €300 more than for the equivalent figure in May 2004.
The report suggest rents have increased in Dublin by on average 12 per cent during the past year, with the increase in Limerick and Cork even higher at 14 per cent.
It found that Dublin 2 remains the most expensive location for renting a two-bedroom property - costing an average of €1,751 a month with Dublin 4 and Dublin 18 averaging €1,694 and €1,602 respectively.
A two-bedroom apartment in Cork city costs on average €1,028, compared to €921 in Galway, €790 in Limerick and €743 in Waterford.
West and North County Dublin remain the most affordable locations in Dublin for a two or three-bedroom property, based on a typical joint application and mortgage interest relief, the report said.
"The surge in the last two and half years is in no small way due to strong demand arising from significantly increased immigration following EU expansion," the report said.
The report also noted that there was a significant drop of 1300 in the number of rental units advertised on Daft.ie this year in comparison with last year which indicates that many tenants may be "staying put" in their accommodation.
Daft.ie said the report's findings marks a total change in mood in the rental market compared to the 2001-2004 period, when rents fell by up to 20 per cent, partly due to the introduction of various section type reliefs, such as the expansion of Section 50 relief for student accommodation and the introduction of the Rent a Room scheme, as well as the prevailing low interest rates.