The tests will be in addition to the pre-departure PCR or antigen test needed to travel to the republic.
In a statement, the Irish government said the first test should be taken on the day of arrival and, if any symptoms emerge or a passenger tests positive from a lateral flow test, they should self-isolate immediately and seek a PCR test.
The latest restrictions come in a bid to control the spread of the Omicron variant of Covid-19.
The taoiseach’s office said it was "taking account of relevant factors", including the intention to continue to align with the European Union’s approach to travel.