More than 82pc of the population classify themselves as "White Irish", followed by "any other white background", the Census 2016 says.
The vast majority (94.1pc) of 'White Irish' people were born in Ireland, and of the 5.9pc, or 226,000, of them born elsewhere, most were born in Britain or Northern Ireland.
The Central Statistics Office also says that more than a third (38pc) of the 22,331 people here with African ethnicity were born in Ireland. Many other Africans living here were born in Nigeria, at 27.2pc.
Overall, the ethnic make-up of the State is changing.
"Large increases can be seen in the number and proportion of Irish nationals with an ethnicity other than 'White Irish'," the CSO said.
"These changes may be explained by the increase in persons granted Irish citizenship since 2011 and by the large increase in those with dual Irish nationality."
The numbers with dual citizenship almost doubled to 105,000 in 2016, up from 55,905 in 2011.
Travellers make up 0.7pc of the population, while Chinese (19,447) make up just 0.4pc.