The new measures, while will apply to arrivals from England, Wales and Scotland, will come into effect on Saturday (9 January).
They will also apply to those whose journey originated in South Africa.
Arrivals will also be advised to self-isolate for 14 days upon their arrival in Ireland.
In a statement, Ireland’s Department for Foreign Affairs said: "From 9 January onwards, any passengers arriving into Ireland whose journey originated in Great Britain or South Africa are required to have a negative / not detected result from a pre-departure Covid-19 PCR test taken within 72 hours before their arrival in Ireland.
"These people will also be advised to self-isolate for 14 days upon arrival in Ireland."
Ryanair issued a statement in response to warn passengers of the new rules.
"If you are travelling from the UK to Ireland you must be in receipt of a negative PCR Covid test result within 72 hours of departure," said the budget carrier.
"You are required to present evidence of your negative test at departure (email, text message, document).
"Upon arrival in Ireland, you are advised to self-isolate for 14 days and to take a further PCR test on or after five days following your arrival.
"Your failure to produce confirmation of a negative PCR test may result in prosecution on arrival into Ireland."