All passengers arriving into the state must have either a negative antigen or PCR test to gain entry into the country from Friday.
Minister for Health Stephen Donnelly confirmed that this would include passengers coming by air or sea from Great Britain, but the rule will not apply to Northern Ireland.
Unvaccinated people will have to have a negative PCR test but fully vaccinated people can avail of a PCR or antigen test.
The tests will have to be privately paid for and cannot be home antigen tests.
Those travelling with an antigen test result will need to have obtained it within 48 hours of departure.
Those with a PCR test result will have a longer pre-travel window of 72 hours.
Legislation allowing for the re-introduction of mandatory hotel quarantine will be tabled on Thursday.
Airlines and ferry companies are in talks with the Department of Transport to discuss checks before people board Ireland-bound flights or boats.
The cabinet also agreed that both children and adults should minimise their social contacts in the weeks ahead to stop the spread of the virus, with children over nine years old advised to wear face coverings at school and on public transport.