The government of the Republic of Ireland has agreed to a “green list” of 15 countries that people can go to.
People returning from these countries will not have to self-isolate for 14 days.
The 15 countries are Malta, Finland, Norway, Italy, Hungary, Estonia, Latvia, Lithuania, Cyprus, Slovakia, Greece, Greenland, Gibraltar, Monaco and San Marino.
Great Britain is not on the list which will be reviewed every two weeks.
General advice for avoiding non-essential travel will apply to all other countries.
Currently, travelers arriving in the Republic of Ireland from any country other than Northern Ireland are required to self-isolate and limit their movements for 14 days.
Speaking in the Dáil on Tuesday afternoon, Taoiseach (Irish Prime Minister) Micheál Martin said he would take a “cautious approach” on overseas travel.
Irish broadcaster RTÉ reported that Tánaiste (Deputy Prime Minister) Leo Varadkar had questioned whether a green list of countries should be published, if the official advice against all non-essential travel should remain in place.
A spokesperson for Mr Varadkar said he believed it was wrong to send conflicting messages about international travel.
The Irish cabinet met late at night at Dublin Castle on Tuesday, with news of the list emerging just before midnight.