New figures show that the total number of trips to Ireland increased by 16% to 2,062,500 in the months from February to April.
The Central Statistics Office figures reveal that trips by UK residents to Ireland rose by 18.6% to 958,100. The UK is the country's largest market for overseas tourism.
The CSO said that trips by residents of European Countries grew by 13.3% to 725,700, while visits here from US residents increased by 19.9% to 284,800 and trips to Ireland from other areas around the globe rose by 1.5% to 94,000.
Meanwhile, the total number of overseas trips made by Irish residents during February to April increased by 6.7% to 1,553,200.
Commenting on today's figures, Niall Gibbons, CEO of Tourism Ireland, said that they represent an "excellent" start to the year.
"Our aim is to ensure that 2016 is another record-breaking year for Irish tourism and already we have seen an exceptional performance from North America for the three-month period of February to April - up almost 20% on the same three-month period in 2015," he added.
Mr Gibbons also noted that Ireland now welcomes 10% of all American visitors to Europe, which he said was particularly noteworthy given the intense competition from other destinations.